LMFDB - Embedded newform 588.2.o.d.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(19,588)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("588.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.562828176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 $ x^8 - 2x^7 + x^6 + 2x^5 - 6x^4 + 4x^3 + 4x^2 - 16x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.4
Root			$0.0777157 - 1.41208i$ of defining polynomial
Character	$\chi$	$=$	588.19
Dual form			588.2.o.d.31.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26175 + 0.638735i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.18404 + 1.61185i) q^{4} +(-0.380152 - 0.219481i) q^{5} +(0.0777157 + 1.41208i) q^{6} +(0.464416 + 2.79004i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.26175 + 0.638735i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.18404 + 1.61185i) q^{4} +(-0.380152 - 0.219481i) q^{5} +(0.0777157 + 1.41208i) q^{6} +(0.464416 + 2.79004i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.339468 - 0.519747i) q^{10} +(-1.83249 + 1.05799i) q^{11} +(-0.803884 + 1.83133i) q^{12} +3.84803i q^{13} -0.438962i q^{15} +(-1.19612 + 3.81698i) q^{16} +(4.89158 - 2.82415i) q^{17} +(-1.18404 + 0.773342i) q^{18} +(-1.48792 + 2.57715i) q^{19} +(-0.0963438 - 0.872621i) q^{20} +(-2.98792 + 0.164445i) q^{22} +(4.13127 + 2.38519i) q^{23} +(-2.18404 + 1.79722i) q^{24} +(-2.40366 - 4.16325i) q^{25} +(-2.45787 + 4.85526i) q^{26} -1.00000 q^{27} +7.02285 q^{29} +(0.280380 - 0.553861i) q^{30} +(-3.71264 - 6.43048i) q^{31} +(-3.94724 + 4.05208i) q^{32} +(-1.83249 - 1.05799i) q^{33} +(7.97584 - 0.438962i) q^{34} +(-1.98792 + 0.219481i) q^{36} +(2.64335 - 4.57842i) q^{37} +(-3.52350 + 2.30134i) q^{38} +(-3.33249 + 1.92401i) q^{39} +(0.435811 - 1.16257i) q^{40} -6.81813i q^{41} +4.38646i q^{43} +(-3.87505 - 1.70100i) q^{44} +(0.380152 - 0.219481i) q^{45} +(3.68914 + 5.64831i) q^{46} +(-0.844569 + 1.46284i) q^{47} +(-3.90366 + 0.872621i) q^{48} +(-0.373604 - 6.78829i) q^{50} +(4.89158 + 2.82415i) q^{51} +(-6.20244 + 4.55620i) q^{52} +(-5.35599 - 9.27685i) q^{53} +(-1.26175 - 0.638735i) q^{54} +0.928833 q^{55} -2.97584 q^{57} +(8.86109 + 4.48574i) q^{58} +(4.05909 + 7.03055i) q^{59} +(0.707540 - 0.519747i) q^{60} +(-5.35787 - 3.09337i) q^{61} +(-0.577061 - 10.4851i) q^{62} +(-7.56863 + 2.59148i) q^{64} +(0.844569 - 1.46284i) q^{65} +(-1.63637 - 2.50539i) q^{66} +(6.79878 - 3.92528i) q^{67} +(10.3439 + 4.54058i) q^{68} +4.77038i q^{69} -1.16982i q^{71} +(-2.64845 - 0.992823i) q^{72} +(8.69036 - 5.01738i) q^{73} +(6.25965 - 4.08843i) q^{74} +(2.40366 - 4.16325i) q^{75} +(-5.91574 + 0.653140i) q^{76} +(-5.43371 + 0.299052i) q^{78} +(-13.4958 - 7.79180i) q^{79} +(1.29246 - 1.18851i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.35498 - 8.60279i) q^{82} +5.49645 q^{83} -2.47939 q^{85} +(-2.80178 + 5.53462i) q^{86} +(3.51142 + 6.08197i) q^{87} +(-3.80287 - 4.62137i) q^{88} +(9.02285 + 5.20934i) q^{89} +(0.619848 - 0.0341142i) q^{90} +(1.04701 + 9.48314i) q^{92} +(3.71264 - 6.43048i) q^{93} +(-2.00000 + 1.30628i) q^{94} +(1.13127 - 0.653140i) q^{95} +(-5.48282 - 1.39237i) q^{96} -2.22605i q^{97} -2.11598i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 4 q^{3} - q^{4} + 2 q^{6} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + q^2 + 4 * q^3 - q^4 + 2 * q^6 + 4 * q^8 - 4 * q^9	$ 8 q + q^{2} + 4 q^{3} - q^{4} + 2 q^{6} + 4 q^{8} - 4 q^{9} + 5 q^{10} + 6 q^{11} + q^{12} - 17 q^{16} + q^{18} + 6 q^{19} - 22 q^{20} - 6 q^{22} - 7 q^{24} + 2 q^{25} - 18 q^{26} - 8 q^{27} - 16 q^{29} + 13 q^{30} - 6 q^{31} - 9 q^{32} + 6 q^{33} + 28 q^{34} + 2 q^{36} + 6 q^{37} - 10 q^{38} - 6 q^{39} + 17 q^{40} - 23 q^{44} + 24 q^{46} - 4 q^{47} - 10 q^{48} + 2 q^{50} - 16 q^{52} - 4 q^{53} - q^{54} + 8 q^{55} + 12 q^{57} + 37 q^{58} + 14 q^{59} - 23 q^{60} - 12 q^{61} + 48 q^{62} + 2 q^{64} + 4 q^{65} + 15 q^{66} + 42 q^{67} + 26 q^{68} - 11 q^{72} + 18 q^{73} - 10 q^{74} - 2 q^{75} - 44 q^{76} - 6 q^{78} - 6 q^{79} + 39 q^{80} - 4 q^{81} + 10 q^{82} - 4 q^{83} - 32 q^{85} + 36 q^{86} - 8 q^{87} - 37 q^{88} + 8 q^{90} - 28 q^{92} + 6 q^{93} - 16 q^{94} - 24 q^{95} - 21 q^{96}+O(q^{100}) $ 8 * q + q^2 + 4 * q^3 - q^4 + 2 * q^6 + 4 * q^8 - 4 * q^9 + 5 * q^10 + 6 * q^11 + q^12 - 17 * q^16 + q^18 + 6 * q^19 - 22 * q^20 - 6 * q^22 - 7 * q^24 + 2 * q^25 - 18 * q^26 - 8 * q^27 - 16 * q^29 + 13 * q^30 - 6 * q^31 - 9 * q^32 + 6 * q^33 + 28 * q^34 + 2 * q^36 + 6 * q^37 - 10 * q^38 - 6 * q^39 + 17 * q^40 - 23 * q^44 + 24 * q^46 - 4 * q^47 - 10 * q^48 + 2 * q^50 - 16 * q^52 - 4 * q^53 - q^54 + 8 * q^55 + 12 * q^57 + 37 * q^58 + 14 * q^59 - 23 * q^60 - 12 * q^61 + 48 * q^62 + 2 * q^64 + 4 * q^65 + 15 * q^66 + 42 * q^67 + 26 * q^68 - 11 * q^72 + 18 * q^73 - 10 * q^74 - 2 * q^75 - 44 * q^76 - 6 * q^78 - 6 * q^79 + 39 * q^80 - 4 * q^81 + 10 * q^82 - 4 * q^83 - 32 * q^85 + 36 * q^86 - 8 * q^87 - 37 * q^88 + 8 * q^90 - 28 * q^92 + 6 * q^93 - 16 * q^94 - 24 * q^95 - 21 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.26175	+	0.638735i	0.892193	+	0.451654i
$2$	1.26175	+	0.638735i	0.892193	+	0.451654i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	1.18404	+	1.61185i	0.592018	+	0.805925i
$5$	−0.380152	−	0.219481i	−0.170009	−	0.0981549i	0.412581	−	0.910921i	$-0.364627\pi$
$5$	−0.380152	−	0.219481i	−0.170009	−	0.0981549i	−0.582590	+	0.812766i	$0.697961\pi$
$6$	0.0777157	+	1.41208i	0.0317273	+	0.576478i
$7$		0			0
$7$		0			0
$8$	0.464416	+	2.79004i	0.164196	+	0.986428i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.339468	−	0.519747i	−0.107349	−	0.164358i
$11$	−1.83249	+	1.05799i	−0.552516	+	0.318995i	−0.750136	−	0.661283i	$-0.770012\pi$
$11$	−1.83249	+	1.05799i	−0.552516	+	0.318995i	0.197620	+	0.980279i	$0.436679\pi$
$12$	−0.803884	+	1.83133i	−0.232061	+	0.528659i
$13$			3.84803i			1.06725i	0.845721	+	0.533625i	$0.179171\pi$
$13$			3.84803i			1.06725i	−0.845721	+	0.533625i	$0.820829\pi$
$14$		0			0
$15$		−	0.438962i		−	0.113339i
$16$	−1.19612	+	3.81698i	−0.299029	+	0.954244i
$17$	4.89158	−	2.82415i	1.18638	−	0.684958i	0.228899	−	0.973450i	$-0.426487\pi$
$17$	4.89158	−	2.82415i	1.18638	−	0.684958i	0.957482	+	0.288492i	$0.0931540\pi$
$18$	−1.18404	+	0.773342i	−0.279080	+	0.182278i
$19$	−1.48792	+	2.57715i	−0.341352	+	0.591240i	−0.984684	−	0.174348i	$-0.944218\pi$
$19$	−1.48792	+	2.57715i	−0.341352	+	0.591240i	0.643332	+	0.765588i	$0.277552\pi$
$20$	−0.0963438	−	0.872621i	−0.0215431	−	0.195124i
$21$		0			0
$22$	−2.98792	+	0.164445i	−0.637027	+	0.0350597i
$23$	4.13127	+	2.38519i	0.861430	+	0.497347i	0.864491	−	0.502649i	$-0.167641\pi$
$23$	4.13127	+	2.38519i	0.861430	+	0.497347i	−0.00306100	+	0.999995i	$0.500974\pi$
$24$	−2.18404	+	1.79722i	−0.445815	+	0.366855i
$25$	−2.40366	−	4.16325i	−0.480731	−	0.832651i
$26$	−2.45787	+	4.85526i	−0.482028	+	0.952194i
$27$	−1.00000			−0.192450
$28$		0			0
$29$	7.02285			1.30411			0.652055	−	0.758172i	$-0.273907\pi$
$29$	7.02285			1.30411			0.652055	+	0.758172i	$0.273907\pi$
$30$	0.280380	−	0.553861i	0.0511902	−	0.101121i
$31$	−3.71264	−	6.43048i	−0.666810	−	1.15495i	−0.978791	−	0.204861i	$-0.934326\pi$
$31$	−3.71264	−	6.43048i	−0.666810	−	1.15495i	0.311981	−	0.950088i	$-0.399007\pi$
$32$	−3.94724	+	4.05208i	−0.697779	+	0.716313i
$33$	−1.83249	−	1.05799i	−0.318995	−	0.184172i
$34$	7.97584	−	0.438962i	1.36785	−	0.0752813i
$35$		0			0
$36$	−1.98792	+	0.219481i	−0.331320	+	0.0365802i
$37$	2.64335	−	4.57842i	0.434564	−	0.752688i	−0.562696	−	0.826664i	$-0.690236\pi$
$37$	2.64335	−	4.57842i	0.434564	−	0.752688i	0.997260	+	0.0739766i	$0.0235690\pi$
$38$	−3.52350	+	2.30134i	−0.571588	+	0.373327i
$39$	−3.33249	+	1.92401i	−0.533625	+	0.308089i
$40$	0.435811	−	1.16257i	0.0689078	−	0.183818i
$41$		−	6.81813i		−	1.06481i	−0.846489	−	0.532407i	$-0.821288\pi$
$41$		−	6.81813i		−	1.06481i	0.846489	−	0.532407i	$-0.178712\pi$
$42$		0			0
$43$			4.38646i			0.668928i	0.942408	+	0.334464i	$0.108555\pi$
$43$			4.38646i			0.668928i	−0.942408	+	0.334464i	$0.891445\pi$
$44$	−3.87505	−	1.70100i	−0.584186	−	0.256435i
$45$	0.380152	−	0.219481i	0.0566697	−	0.0327183i
$46$	3.68914	+	5.64831i	0.543934	+	0.832797i
$47$	−0.844569	+	1.46284i	−0.123193	+	0.213377i	−0.921025	−	0.389503i	$-0.872647\pi$
$47$	−0.844569	+	1.46284i	−0.123193	+	0.213377i	0.797832	+	0.602880i	$0.205980\pi$
$48$	−3.90366	+	0.872621i	−0.563444	+	0.125952i
$49$		0			0
$50$	−0.373604	−	6.78829i	−0.0528355	−	0.960010i
$51$	4.89158	+	2.82415i	0.684958	+	0.395461i
$52$	−6.20244	+	4.55620i	−0.860124	+	0.631832i
$53$	−5.35599	−	9.27685i	−0.735702	−	1.27427i	−0.954415	−	0.298484i	$-0.903519\pi$
$53$	−5.35599	−	9.27685i	−0.735702	−	1.27427i	0.218712	−	0.975789i	$-0.429814\pi$
$54$	−1.26175	−	0.638735i	−0.171703	−	0.0869208i
$55$	0.928833			0.125244
$56$		0			0
$57$	−2.97584			−0.394160
$58$	8.86109	+	4.48574i	1.16352	+	0.589006i
$59$	4.05909	+	7.03055i	0.528448	+	0.915299i	0.999450	+	0.0331668i	$0.0105593\pi$
$59$	4.05909	+	7.03055i	0.528448	+	0.915299i	−0.471002	+	0.882132i	$0.656107\pi$
$60$	0.707540	−	0.519747i	0.0913431	−	0.0670990i
$61$	−5.35787	−	3.09337i	−0.686005	−	0.396065i	0.116109	−	0.993237i	$-0.462958\pi$
$61$	−5.35787	−	3.09337i	−0.686005	−	0.396065i	−0.802114	+	0.597171i	$0.796291\pi$
$62$	−0.577061	−	10.4851i	−0.0732868	−	1.33160i
$63$		0			0
$64$	−7.56863	+	2.59148i	−0.946079	+	0.323935i
$65$	0.844569	−	1.46284i	0.104756	−	0.181442i
$66$	−1.63637	−	2.50539i	−0.201424	−	0.308393i
$67$	6.79878	−	3.92528i	0.830604	−	0.479549i	−0.0234557	−	0.999725i	$-0.507467\pi$
$67$	6.79878	−	3.92528i	0.830604	−	0.479549i	0.854059	+	0.520176i	$0.174134\pi$
$68$	10.3439	+	4.54058i	1.25438	+	0.550627i
$69$			4.77038i			0.574287i
$70$		0			0
$71$		−	1.16982i		−	0.138833i	−0.997588	−	0.0694163i	$-0.977886\pi$
$71$		−	1.16982i		−	0.138833i	0.997588	−	0.0694163i	$-0.0221137\pi$
$72$	−2.64845	−	0.992823i	−0.312123	−	0.117005i
$73$	8.69036	−	5.01738i	1.01713	−	0.587240i	0.103858	−	0.994592i	$-0.466881\pi$
$73$	8.69036	−	5.01738i	1.01713	−	0.587240i	0.913271	+	0.407352i	$0.133548\pi$
$74$	6.25965	−	4.08843i	0.727669	−	0.475270i
$75$	2.40366	−	4.16325i	0.277550	−	0.480731i
$76$	−5.91574	+	0.653140i	−0.678581	+	0.0749203i
$77$		0			0
$78$	−5.43371	+	0.299052i	−0.615246	+	0.0338610i
$79$	−13.4958	−	7.79180i	−1.51840	−	0.876646i	−0.999766	−	0.0216472i	$-0.993109\pi$
$79$	−13.4958	−	7.79180i	−1.51840	−	0.876646i	−0.518630	−	0.854999i	$-0.673558\pi$
$80$	1.29246	−	1.18851i	0.144501	−	0.132879i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.35498	−	8.60279i	0.480927	−	0.950019i
$83$	5.49645			0.603314			0.301657	−	0.953417i	$-0.402460\pi$
$83$	5.49645			0.603314			0.301657	+	0.953417i	$0.402460\pi$
$84$		0			0
$85$	−2.47939			−0.268928
$86$	−2.80178	+	5.53462i	−0.302124	+	0.596814i
$87$	3.51142	+	6.08197i	0.376464	+	0.652055i
$88$	−3.80287	−	4.62137i	−0.405387	−	0.492640i
$89$	9.02285	+	5.20934i	0.956420	+	0.552189i	0.895069	−	0.445927i	$-0.147126\pi$
$89$	9.02285	+	5.20934i	0.956420	+	0.552189i	0.0613507	+	0.998116i	$0.480459\pi$
$90$	0.619848	−	0.0341142i	0.0653377	−	0.00359595i
$91$		0			0
$92$	1.04701	+	9.48314i	0.109158	+	0.988686i
$93$	3.71264	−	6.43048i	0.384983	−	0.666810i
$94$	−2.00000	+	1.30628i	−0.206284	+	0.134733i
$95$	1.13127	−	0.653140i	0.116066	−	0.0670108i
$96$	−5.48282	−	1.39237i	−0.559588	−	0.142108i
$97$		−	2.22605i		−	0.226021i	−0.993594	−	0.113011i	$-0.963951\pi$
$97$		−	2.22605i		−	0.226021i	0.993594	−	0.113011i	$-0.0360494\pi$
$98$		0			0
$99$		−	2.11598i		−	0.212664i
$100$	3.86452	−	8.80378i	0.386452	−	0.880378i
$101$	0.664978	−	0.383925i	0.0661678	−	0.0382020i	−0.466551	−	0.884494i	$-0.654504\pi$
$101$	0.664978	−	0.383925i	0.0661678	−	0.0382020i	0.532719	+	0.846292i	$0.321170\pi$
$102$	4.36807	+	6.68780i	0.432504	+	0.662191i
$103$	−4.31939	+	7.48141i	−0.425602	+	0.737165i	−0.996476	−	0.0838727i	$-0.973271\pi$
$103$	−4.31939	+	7.48141i	−0.425602	+	0.737165i	0.570874	+	0.821038i	$0.306604\pi$
$104$	−10.7361	+	1.78709i	−1.05277	+	0.175238i
$105$		0			0
$106$	−0.832489	−	15.1261i	−0.0808585	−	1.46918i
$107$	−2.20346	−	1.27217i	−0.213016	−	0.122985i	0.389696	−	0.920943i	$-0.372580\pi$
$107$	−2.20346	−	1.27217i	−0.213016	−	0.122985i	−0.602712	+	0.797959i	$0.705913\pi$
$108$	−1.18404	−	1.61185i	−0.113934	−	0.155100i
$109$	3.40366	+	5.89531i	0.326011	+	0.564668i	0.981716	−	0.190349i	$-0.0609620\pi$
$109$	3.40366	+	5.89531i	0.326011	+	0.564668i	−0.655705	+	0.755017i	$0.727629\pi$
$110$	1.17196	+	0.593278i	0.111742	+	0.0565668i
$111$	5.28670			0.501792
$112$		0			0
$113$	13.6408			1.28322			0.641610	−	0.767031i	$-0.278267\pi$
$113$	13.6408			1.28322			0.641610	+	0.767031i	$0.278267\pi$
$114$	−3.75477	−	1.90077i	−0.351667	−	0.178024i
$115$	−1.04701	−	1.81347i	−0.0976340	−	0.169107i
$116$	8.31531	+	11.3198i	0.772057	+	1.05101i
$117$	−3.33249	−	1.92401i	−0.308089	−	0.177875i
$118$	0.630909	+	11.4635i	0.0580799	+	1.05530i
$119$		0			0
$120$	1.22472	−	0.203861i	0.111801	−	0.0186099i
$121$	−3.26132	+	5.64878i	−0.296484	+	0.513525i
$122$	−4.78446	−	7.32532i	−0.433165	−	0.663203i
$123$	5.90467	−	3.40907i	0.532407	−	0.307385i
$124$	5.96907	−	13.5981i	0.536038	−	1.22115i
$125$			4.30504i			0.385054i
$126$		0			0
$127$		−	3.51914i		−	0.312273i	−0.987735	−	0.156137i	$-0.950096\pi$
$127$		−	3.51914i		−	0.312273i	0.987735	−	0.156137i	$-0.0499040\pi$
$128$	−11.2050	−	1.56454i	−0.990392	−	0.138287i
$129$	−3.79878	+	2.19323i	−0.334464	+	0.193103i
$130$	2.00000	−	1.30628i	0.175412	−	0.114568i
$131$	9.80833	−	16.9885i	0.856958	−	1.48429i	−0.0178590	−	0.999841i	$-0.505685\pi$
$131$	9.80833	−	16.9885i	0.856958	−	1.48429i	0.874817	−	0.484454i	$-0.160982\pi$
$132$	−0.464416	−	4.20639i	−0.0404223	−	0.366119i
$133$		0			0
$134$	11.0856	−	0.610111i	0.957649	−	0.0527056i
$135$	0.380152	+	0.219481i	0.0327183	+	0.0188899i
$136$	10.1512	+	12.3361i	0.870460	+	1.05781i
$137$	1.68914	+	2.92567i	0.144313	+	0.249957i	0.929116	−	0.369788i	$-0.120570\pi$
$137$	1.68914	+	2.92567i	0.144313	+	0.249957i	−0.784804	+	0.619745i	$0.787236\pi$
$138$	−3.04701	+	6.01904i	−0.259379	+	0.512375i
$139$	−16.4481			−1.39511			−0.697556	−	0.716530i	$-0.745729\pi$
$139$	−16.4481			−1.39511			−0.697556	+	0.716530i	$0.745729\pi$
$140$		0			0
$141$	−1.68914			−0.142251
$142$	0.747207	−	1.47603i	0.0627042	−	0.123866i
$143$	−4.07117	−	7.05147i	−0.340448	−	0.589673i
$144$	−2.70754	−	2.94435i	−0.225628	−	0.245363i
$145$	−2.66975	−	1.54138i	−0.221711	−	0.128005i
$146$	14.1699	−	0.779858i	1.17271	−	0.0645415i
$147$		0			0
$148$	10.5095	−	1.16033i	0.863879	−	0.0953786i
$149$	−3.23970	+	5.61132i	−0.265406	+	0.459697i	−0.967670	−	0.252220i	$-0.918839\pi$
$149$	−3.23970	+	5.61132i	−0.265406	+	0.459697i	0.702264	+	0.711917i	$0.252173\pi$
$150$	5.69203	−	3.71770i	0.464753	−	0.303549i
$151$	−6.72827	+	3.88457i	−0.547539	+	0.316122i	−0.748129	−	0.663554i	$-0.769047\pi$
$151$	−6.72827	+	3.88457i	−0.547539	+	0.316122i	0.200590	+	0.979675i	$0.435714\pi$
$152$	−7.88137	−	2.95448i	−0.639264	−	0.239640i
$153$			5.64831i			0.456639i
$154$		0			0
$155$			3.25942i			0.261803i
$156$	−7.04701	−	3.09337i	−0.564212	−	0.247668i
$157$	−7.32996	+	4.23195i	−0.584994	+	0.337747i	−0.763116	−	0.646262i	$-0.776331\pi$
$157$	−7.32996	+	4.23195i	−0.584994	+	0.337747i	0.178121	+	0.984009i	$0.442998\pi$
$158$	−12.0515	−	18.4516i	−0.958762	−	1.46793i
$159$	5.35599	−	9.27685i	0.424758	−	0.735702i
$160$	2.38990	−	0.674063i	0.188939	−	0.0532893i
$161$		0			0
$162$	−0.0777157	−	1.41208i	−0.00610592	−	0.110943i
$163$	−6.02285	−	3.47729i	−0.471746	−	0.272363i	0.245224	−	0.969466i	$-0.421138\pi$
$163$	−6.02285	−	3.47729i	−0.471746	−	0.272363i	−0.716970	+	0.697104i	$0.754472\pi$
$164$	10.9898	−	8.07291i	0.858159	−	0.630389i
$165$	0.464416	+	0.804393i	0.0361548	+	0.0626219i
$166$	6.93516	+	3.51077i	0.538273	+	0.272489i
$167$	−8.12021			−0.628361			−0.314180	−	0.949363i	$-0.601730\pi$
$167$	−8.12021			−0.628361			−0.314180	+	0.949363i	$0.601730\pi$
$168$		0			0
$169$	−1.80731			−0.139024
$170$	−3.12838	−	1.58367i	−0.239936	−	0.121462i
$171$	−1.48792	−	2.57715i	−0.113784	−	0.197080i
$172$	−7.07031	+	5.19372i	−0.539106	+	0.396018i
$173$	1.22660	+	0.708177i	0.0932565	+	0.0538417i	0.545903	−	0.837848i	$-0.316187\pi$
$173$	1.22660	+	0.708177i	0.0932565	+	0.0538417i	−0.452646	+	0.891690i	$0.649520\pi$
$174$	0.545785	+	9.91680i	0.0413759	+	0.751791i
$175$		0			0
$176$	−1.84645	−	8.26004i	−0.139181	−	0.622624i
$177$	−4.05909	+	7.03055i	−0.305100	+	0.528448i
$178$	8.05721	+	12.3361i	0.603913	+	0.924630i
$179$	9.29401	−	5.36590i	0.694667	−	0.401066i	−0.110691	−	0.993855i	$-0.535306\pi$
$179$	9.29401	−	5.36590i	0.694667	−	0.401066i	0.805358	+	0.592789i	$0.201973\pi$
$180$	0.803884	+	0.352875i	0.0599180	+	0.0263017i
$181$		−	1.21426i		−	0.0902549i	−0.998981	−	0.0451275i	$-0.985631\pi$
$181$		−	1.21426i		−	0.0902549i	0.998981	−	0.0451275i	$-0.0143694\pi$
$182$		0			0
$183$		−	6.18674i		−	0.457337i
$184$	−4.73615	+	12.6341i	−0.349153	+	0.931401i
$185$	−2.00975	+	1.16033i	−0.147760	+	0.0853092i
$186$	8.79180	−	5.74228i	0.644646	−	0.421045i
$187$	−5.97584	+	10.3505i	−0.436997	+	0.756901i
$188$	−3.35787	+	0.370733i	−0.244898	+	0.0270385i
$189$		0			0
$190$	1.84457	−	0.101518i	0.133819	−	0.00736493i
$191$	5.67473	+	3.27631i	0.410609	+	0.237065i	0.691051	−	0.722806i	$-0.257148\pi$
$191$	5.67473	+	3.27631i	0.410609	+	0.237065i	−0.280442	+	0.959871i	$0.590481\pi$
$192$	−6.02861	−	5.25889i	−0.435077	−	0.379528i
$193$	1.61818	+	2.80276i	0.116479	+	0.201747i	0.918370	−	0.395723i	$-0.129506\pi$
$193$	1.61818	+	2.80276i	0.116479	+	0.201747i	−0.801891	+	0.597470i	$0.796173\pi$
$194$	1.42185	−	2.80872i	0.102083	−	0.201654i
$195$	1.68914			0.120962
$196$		0			0
$197$	−19.2554			−1.37189			−0.685947	−	0.727652i	$-0.740612\pi$
$197$	−19.2554			−1.37189			−0.685947	+	0.727652i	$0.740612\pi$
$198$	1.35155	−	2.66984i	0.0960503	−	0.189737i
$199$	−4.31086	−	7.46663i	−0.305589	−	0.529296i	0.671803	−	0.740730i	$-0.265520\pi$
$199$	−4.31086	−	7.46663i	−0.305589	−	0.529296i	−0.977392	+	0.211434i	$0.932187\pi$
$200$	10.4993	−	8.63978i	0.742416	−	0.610925i
$201$	6.79878	+	3.92528i	0.479549	+	0.276868i
$202$	1.08426	−	0.0596741i	0.0762886	−	0.00419865i
$203$		0			0
$204$	1.23970	+	11.2284i	0.0867961	+	0.786144i
$205$	−1.49645	+	2.59193i	−0.104517	+	0.181028i
$206$	−10.2286	+	6.68073i	−0.712663	+	0.465469i
$207$	−4.13127	+	2.38519i	−0.287143	+	0.165782i
$208$	−14.6878	−	4.60269i	−1.01842	−	0.319139i
$209$		−	6.29681i		−	0.435559i
$210$		0			0
$211$			6.09787i			0.419795i	0.977723	+	0.209897i	$0.0673130\pi$
$211$			6.09787i			0.419795i	−0.977723	+	0.209897i	$0.932687\pi$
$212$	8.61120	−	19.6172i	0.591419	−	1.34731i
$213$	1.01310	−	0.584912i	0.0694163	−	0.0400775i
$214$	−1.96764	−	3.01258i	−0.134505	−	0.205936i
$215$	0.962744	−	1.66752i	0.0656586	−	0.113724i
$216$	−0.464416	−	2.79004i	−0.0315995	−	0.189838i
$217$		0			0
$218$	0.529035	+	9.61245i	0.0358308	+	0.651037i
$219$	8.69036	+	5.01738i	0.587240	+	0.339043i
$220$	1.09977	+	1.49714i	0.0741466	+	0.100937i
$221$	10.8674	+	18.8229i	0.731022	+	1.26617i
$222$	6.67051	+	3.37680i	0.447695	+	0.226636i
$223$	−2.44944			−0.164027			−0.0820134	−	0.996631i	$-0.526135\pi$
$223$	−2.44944			−0.164027			−0.0820134	+	0.996631i	$0.526135\pi$
$224$		0			0
$225$	4.80731			0.320487
$226$	17.2113	+	8.71286i	1.14488	+	0.579571i
$227$	11.6398	+	20.1607i	0.772561	+	1.33811i	0.936155	+	0.351587i	$0.114358\pi$
$227$	11.6398	+	20.1607i	0.772561	+	1.33811i	−0.163595	+	0.986528i	$0.552309\pi$
$228$	−3.52350	−	4.79661i	−0.233350	−	0.317663i
$229$	10.1385	+	5.85346i	0.669970	+	0.386808i	0.796065	−	0.605211i	$-0.206911\pi$
$229$	10.1385	+	5.85346i	0.669970	+	0.386808i	−0.126095	+	0.992018i	$0.540244\pi$
$230$	−0.162738	−	2.95691i	−0.0107306	−	0.194973i
$231$		0			0
$232$	3.26153	+	19.5940i	0.214130	+	1.28641i
$233$	4.08426	−	7.07415i	0.267569	−	0.463443i	−0.700664	−	0.713491i	$-0.747113\pi$
$233$	4.08426	−	7.07415i	0.267569	−	0.463443i	0.968234	+	0.250048i	$0.0804463\pi$
$234$	−2.97584	−	4.55620i	−0.194537	−	0.297848i
$235$	0.642129	−	0.370733i	0.0418879	−	0.0241840i
$236$	−6.52607	+	14.8671i	−0.424811	+	0.967763i
$237$		−	15.5836i		−	1.01226i
$238$		0			0
$239$		−	18.1984i		−	1.17716i	−0.808439	−	0.588579i	$-0.799687\pi$
$239$		−	18.1984i		−	1.17716i	0.808439	−	0.588579i	$-0.200313\pi$
$240$	1.67551	+	0.525049i	0.108154	+	0.0338918i
$241$	−25.0409	+	14.4574i	−1.61303	+	0.931282i	−0.624364	+	0.781133i	$0.714642\pi$
$241$	−25.0409	+	14.4574i	−1.61303	+	0.931282i	−0.988663	+	0.150149i	$0.952025\pi$
$242$	−7.72305	+	5.04424i	−0.496456	+	0.324256i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−1.35787	−	12.2987i	−0.0869288	−	0.787346i
$245$		0			0
$246$	9.62772	−	0.529876i	0.613841	−	0.0337836i
$247$	−9.91696	−	5.72556i	−0.631001	−	0.364309i
$248$	16.2171	−	13.3448i	1.02979	−	0.847398i
$249$	2.74822	+	4.76007i	0.174162	+	0.301657i
$250$	−2.74978	+	5.43189i	−0.173911	+	0.343543i
$251$	20.3586			1.28502			0.642512	−	0.766276i	$-0.277892\pi$
$251$	20.3586			1.28502			0.642512	+	0.766276i	$0.277892\pi$
$252$		0			0
$253$	−10.0940			−0.634605
$254$	2.24780	−	4.44028i	0.141039	−	0.278608i
$255$	−1.23970	−	2.14722i	−0.0776328	−	0.134464i
$256$	−13.1386	−	9.13109i	−0.821163	−	0.570693i
$257$	−18.4350	−	10.6435i	−1.14995	−	0.663922i	−0.201072	−	0.979577i	$-0.564442\pi$
$257$	−18.4350	−	10.6435i	−1.14995	−	0.663922i	−0.948874	+	0.315655i	$0.897776\pi$
$258$	−6.19401	+	0.340896i	−0.385622	+	0.0212233i
$259$		0			0
$260$	3.35787	−	0.370733i	0.208246	−	0.0229919i
$261$	−3.51142	+	6.08197i	−0.217352	+	0.376464i
$262$	23.2268	−	15.1704i	1.43496	−	0.937230i
$263$	−17.4760	+	10.0898i	−1.07762	+	0.622164i	−0.930253	−	0.366918i	$-0.880413\pi$
$263$	−17.4760	+	10.0898i	−1.07762	+	0.622164i	−0.147366	+	0.989082i	$0.547080\pi$
$264$	2.10079	−	5.60406i	0.129295	−	0.344906i
$265$			4.70215i			0.288851i
$266$		0			0
$267$			10.4187i			0.637613i
$268$	14.3770	+	6.31094i	0.878213	+	0.385502i
$269$	−14.1764	+	8.18475i	−0.864351	+	0.499033i	−0.865467	−	0.500966i	$-0.832978\pi$
$269$	−14.1764	+	8.18475i	−0.864351	+	0.499033i	0.00111621	+	0.999999i	$0.499645\pi$
$270$	0.339468	+	0.519747i	0.0206593	+	0.0316308i
$271$	−6.72696	+	11.6514i	−0.408634	+	0.707775i	−0.994737	−	0.102462i	$-0.967328\pi$
$271$	−6.72696	+	11.6514i	−0.408634	+	0.707775i	0.586103	+	0.810236i	$0.300661\pi$
$272$	4.92883	+	22.0490i	0.298854	+	1.33692i
$273$		0			0
$274$	0.262545	+	4.77038i	0.0158609	+	0.288189i
$275$	8.80935	+	5.08608i	0.531224	+	0.306702i
$276$	−7.68914	+	5.64831i	−0.462832	+	0.339988i
$277$	−1.40366	−	2.43120i	−0.0843375	−	0.146077i	0.820771	−	0.571257i	$-0.193544\pi$
$277$	−1.40366	−	2.43120i	−0.0843375	−	0.146077i	−0.905109	+	0.425180i	$0.860211\pi$
$278$	−20.7535	−	10.5060i	−1.24471	−	0.630107i
$279$	7.42528			0.444540
$280$		0			0
$281$	−25.4502			−1.51823			−0.759115	−	0.650957i	$-0.774368\pi$
$281$	−25.4502			−1.51823			−0.759115	+	0.650957i	$0.774368\pi$
$282$	−2.13127	−	1.07891i	−0.126915	−	0.0642482i
$283$	2.36975	+	4.10452i	0.140867	+	0.243988i	0.927823	−	0.373020i	$-0.121678\pi$
$283$	2.36975	+	4.10452i	0.140867	+	0.243988i	−0.786957	+	0.617008i	$0.788344\pi$
$284$	1.88558	−	1.38511i	0.111889	−	0.0821914i
$285$	1.13127	+	0.653140i	0.0670108	+	0.0386887i
$286$	−0.632787	−	11.4976i	−0.0374175	−	0.679867i
$287$		0			0
$288$	−1.53558	−	5.44445i	−0.0904851	−	0.320817i
$289$	7.45168	−	12.9067i	0.438334	−	0.759217i
$290$	−2.38403	−	3.65010i	−0.139995	−	0.214341i
$291$	1.92782	−	1.11302i	0.113011	−	0.0652467i
$292$	18.3770	+	8.06679i	1.07543	+	0.472073i
$293$		−	3.22818i		−	0.188592i	−0.995544	−	0.0942960i	$-0.969940\pi$
$293$		−	3.22818i		−	0.188592i	0.995544	−	0.0942960i	$-0.0300600\pi$
$294$		0			0
$295$		−	3.56357i		−	0.207479i
$296$	14.0016	+	5.24876i	0.813826	+	0.305078i
$297$	1.83249	−	1.05799i	0.106332	−	0.0613907i
$298$	−7.67183	+	5.01079i	−0.444417	+	0.290267i
$299$	−9.17828	+	15.8972i	−0.530794	+	0.919362i
$300$	9.55656	−	1.05511i	0.551748	−	0.0609170i
$301$		0			0
$302$	−10.9706	+	0.603784i	−0.631288	+	0.0347439i
$303$	0.664978	+	0.383925i	0.0382020	+	0.0220559i
$304$	−8.05721	−	8.76193i	−0.462113	−	0.502531i
$305$	1.35787	+	2.35190i	0.0777515	+	0.134669i
$306$	−3.60777	+	7.12676i	−0.206242	+	0.407410i
$307$	−5.45523			−0.311347			−0.155673	−	0.987809i	$-0.549755\pi$
$307$	−5.45523			−0.311347			−0.155673	+	0.987809i	$0.549755\pi$
$308$		0			0
$309$	−8.63878			−0.491443
$310$	−2.08190	+	4.11258i	−0.118244	+	0.233579i
$311$	−15.2625	−	26.4355i	−0.865460	−	1.49902i	−0.866590	−	0.499020i	$-0.833693\pi$
$311$	−15.2625	−	26.4355i	−0.865460	−	1.49902i	0.00113066	−	0.999999i	$-0.499640\pi$
$312$	−6.91574	−	8.40423i	−0.391526	−	0.475796i
$313$	16.3093	+	9.41621i	0.921859	+	0.532235i	0.884228	−	0.467056i	$-0.154685\pi$
$313$	16.3093	+	9.41621i	0.921859	+	0.532235i	0.0376312	+	0.999292i	$0.488019\pi$
$314$	−11.9517	+	0.657778i	−0.674472	+	0.0371206i
$315$		0			0
$316$	−3.42030	−	30.9790i	−0.192407	−	1.74270i
$317$	−8.58259	+	14.8655i	−0.482046	+	0.834929i	−0.999788	−	0.0206085i	$-0.993440\pi$
$317$	−8.58259	+	14.8655i	−0.482046	+	0.834929i	0.517741	+	0.855537i	$0.326773\pi$
$318$	12.6834	−	8.28403i	0.711249	−	0.464545i
$319$	−12.8693	+	7.43009i	−0.720542	+	0.416005i
$320$	3.44601	+	0.676014i	0.192638	+	0.0377904i
$321$		−	2.54433i		−	0.142011i
$322$		0			0
$323$			16.8085i			0.935248i
$324$	0.803884	−	1.83133i	0.0446602	−	0.101741i
$325$	16.0203	−	9.24933i	0.888647	−	0.513061i
$326$	−5.37827	−	8.23448i	−0.297875	−	0.456066i
$327$	−3.40366	+	5.89531i	−0.188223	+	0.326011i
$328$	19.0228	−	3.16645i	1.05036	−	0.174838i
$329$		0			0
$330$	0.0721849	+	1.31158i	0.00397365	+	0.0722003i
$331$	18.6081	+	10.7434i	1.02280	+	0.590511i	0.914912	−	0.403652i	$-0.132259\pi$
$331$	18.6081	+	10.7434i	1.02280	+	0.590511i	0.107883	+	0.994164i	$0.465593\pi$
$332$	6.50800	+	8.85945i	0.357173	+	0.486225i
$333$	2.64335	+	4.57842i	0.144855	+	0.250896i
$334$	−10.2457	−	5.18666i	−0.560619	−	0.283801i
$335$	−3.44610			−0.188280
$336$		0			0
$337$	5.91046			0.321964			0.160982	−	0.986957i	$-0.448534\pi$
$337$	5.91046			0.321964			0.160982	+	0.986957i	$0.448534\pi$
$338$	−2.28038	−	1.15439i	−0.124036	−	0.0627907i
$339$	6.82041	+	11.8133i	0.370434	+	0.641610i
$340$	−2.93569	−	3.99640i	−0.159210	−	0.216735i
$341$	13.6068	+	7.85586i	0.736847	+	0.425419i
$342$	−0.231269	−	4.20212i	−0.0125056	−	0.227224i
$343$		0			0
$344$	−12.2384	+	2.03714i	−0.659850	+	0.109835i
$345$	1.04701	−	1.81347i	0.0563690	−	0.0976340i
$346$	1.09533	+	1.67701i	0.0588851	+	0.0901569i
$347$	−2.43838	+	1.40780i	−0.130899	+	0.0755746i	−0.564020	−	0.825761i	$-0.690746\pi$
$347$	−2.43838	+	1.40780i	−0.130899	+	0.0755746i	0.433121	+	0.901336i	$0.357412\pi$
$348$	−5.64556	+	12.8612i	−0.302634	+	0.689430i
$349$		−	9.54077i		−	0.510705i	−0.966848	−	0.255353i	$-0.917808\pi$
$349$		−	9.54077i		−	0.510705i	0.966848	−	0.255353i	$-0.0821916\pi$
$350$		0			0
$351$		−	3.84803i		−	0.205392i
$352$	2.94622	−	11.6015i	0.157034	−	0.618363i
$353$	−8.63351	+	4.98456i	−0.459516	+	0.265301i	−0.711841	−	0.702341i	$-0.752138\pi$
$353$	−8.63351	+	4.98456i	−0.459516	+	0.265301i	0.252325	+	0.967643i	$0.418805\pi$
$354$	−9.61221	+	6.27813i	−0.510883	+	0.333679i
$355$	−0.256754	+	0.444711i	−0.0136271	+	0.0236028i
$356$	2.28670	+	20.7115i	0.121195	+	1.09771i
$357$		0			0
$358$	15.1541	−	0.834029i	0.800920	−	0.0440798i
$359$	6.00000	+	3.46410i	0.316668	+	0.182828i	0.649906	−	0.760014i	$-0.274808\pi$
$359$	6.00000	+	3.46410i	0.316668	+	0.182828i	−0.333238	+	0.942843i	$0.608141\pi$
$360$	0.788909	+	0.958709i	0.0415792	+	0.0505284i
$361$	5.07218	+	8.78528i	0.266957	+	0.462383i
$362$	0.775587	−	1.53209i	0.0407639	−	0.0805248i
$363$	−6.52264			−0.342350
$364$		0			0
$365$	−4.40488			−0.230562
$366$	3.95168	−	7.80613i	0.206558	−	0.408033i
$367$	−8.95234	−	15.5059i	−0.467308	−	0.809402i	0.531994	−	0.846748i	$-0.321443\pi$
$367$	−8.95234	−	15.5059i	−0.467308	−	0.809402i	−0.999302	+	0.0373465i	$0.988109\pi$
$368$	−14.0457	+	12.9160i	−0.732183	+	0.673293i
$369$	5.90467	+	3.40907i	0.307385	+	0.177469i
$370$	−3.27695	+	0.180352i	−0.170361	+	0.00937604i
$371$		0			0
$372$	14.7609	−	1.62971i	0.765316	−	0.0844964i
$373$	−7.23716	+	12.5351i	−0.374726	+	0.649045i	−0.990286	−	0.139045i	$-0.955597\pi$
$373$	−7.23716	+	12.5351i	−0.374726	+	0.649045i	0.615560	+	0.788090i	$0.288930\pi$
$374$	−14.1512	+	9.24274i	−0.731742	+	0.477931i
$375$	−3.72827	+	2.15252i	−0.192527	+	0.111156i
$376$	−4.47360	−	1.67701i	−0.230708	−	0.0864854i
$377$			27.0241i			1.39181i
$378$		0			0
$379$			21.5969i			1.10936i	0.832064	+	0.554679i	$0.187159\pi$
$379$			21.5969i			1.10936i	−0.832064	+	0.554679i	$0.812841\pi$
$380$	2.39223	+	1.05010i	0.122719	+	0.0538689i
$381$	3.04766	−	1.75957i	0.156137	−	0.0901455i
$382$	5.06741	+	7.75853i	0.259271	+	0.396961i
$383$	0.318169	−	0.551085i	0.0162577	−	0.0281591i	−0.857782	−	0.514013i	$-0.828158\pi$
$383$	0.318169	−	0.551085i	0.0162577	−	0.0281591i	0.874040	+	0.485854i	$0.161491\pi$
$384$	−4.24757	−	10.4861i	−0.216758	−	0.535116i
$385$		0			0
$386$	0.251515	+	4.56997i	0.0128018	+	0.232606i
$387$	−3.79878	−	2.19323i	−0.193103	−	0.111488i
$388$	3.58806	−	2.63572i	0.182156	−	0.133809i
$389$	0.509547	+	0.882561i	0.0258351	+	0.0447476i	0.878654	−	0.477459i	$-0.158442\pi$
$389$	0.509547	+	0.882561i	0.0258351	+	0.0447476i	−0.852819	+	0.522207i	$0.825109\pi$
$390$	2.13127	+	1.07891i	0.107921	+	0.0546327i
$391$	26.9446			1.36265
$392$		0			0
$393$	19.6167			0.989530
$394$	−24.2956	−	12.2991i	−1.22399	−	0.619621i
$395$	3.42030	+	5.92414i	0.172094	+	0.298076i
$396$	3.41063	−	2.50539i	0.171391	−	0.125901i
$397$	−25.8035	−	14.8976i	−1.29504	−	0.747691i	−0.315496	−	0.948927i	$-0.602171\pi$
$397$	−25.8035	−	14.8976i	−1.29504	−	0.747691i	−0.979543	+	0.201236i	$0.935504\pi$
$398$	−0.670043	−	12.1745i	−0.0335862	−	0.610254i
$399$		0			0
$400$	18.7661	−	4.19496i	0.938305	−	0.209748i
$401$	3.39513	−	5.88053i	0.169545	−	0.293660i	−0.768715	−	0.639591i	$-0.779104\pi$
$401$	3.39513	−	5.88053i	0.169545	−	0.293660i	0.938260	+	0.345931i	$0.112437\pi$
$402$	6.07117	+	9.29535i	0.302802	+	0.463610i
$403$	24.7447	−	14.2863i	1.23262	−	0.711654i
$404$	1.40619	+	0.617263i	0.0699605	+	0.0307100i
$405$			0.438962i			0.0218122i
$406$		0			0
$407$			11.1865i			0.554496i
$408$	−5.60777	+	14.9593i	−0.277626	+	0.740594i
$409$	−3.21574	+	1.85661i	−0.159008	+	0.0918034i	−0.577393	−	0.816467i	$-0.695930\pi$
$409$	−3.21574	+	1.85661i	−0.159008	+	0.0918034i	0.418384	+	0.908270i	$0.362596\pi$
$410$	−3.54370	+	2.31454i	−0.175011	+	0.114307i
$411$	−1.68914	+	2.92567i	−0.0833190	+	0.144313i
$412$	−17.1732	+	1.89605i	−0.846064	+	0.0934116i
$413$		0			0
$414$	−6.73615	+	0.370733i	−0.331063	+	0.0182206i
$415$	−2.08949	−	1.20637i	−0.102569	−	0.0592182i
$416$	−15.5925	−	15.1891i	−0.764485	−	0.744705i
$417$	−8.22407	−	14.2445i	−0.402734	−	0.697556i
$418$	4.02199	−	7.94501i	0.196722	−	0.388603i
$419$	−20.7082			−1.01166			−0.505832	−	0.862632i	$-0.668814\pi$
$419$	−20.7082			−1.01166			−0.505832	+	0.862632i	$0.668814\pi$
$420$		0			0
$421$	15.6579			0.763118			0.381559	−	0.924344i	$-0.375387\pi$
$421$	15.6579			0.763118			0.381559	+	0.924344i	$0.375387\pi$
$422$	−3.89492	+	7.69400i	−0.189602	+	0.374538i
$423$	−0.844569	−	1.46284i	−0.0410643	−	0.0711255i
$424$	23.3954	−	19.2518i	1.13618	−	0.934948i
$425$	−23.5153	−	13.5766i	−1.14066	−	0.658561i
$426$	1.65188	−	0.0909137i	0.0800339	−	0.00440478i
$427$		0			0
$428$	−0.558433	−	5.05793i	−0.0269929	−	0.244484i
$429$	4.07117	−	7.05147i	0.196558	−	0.340448i
$430$	2.27985	−	1.48906i	0.109944	−	0.0718089i
$431$	10.2723	−	5.93071i	0.494799	−	0.285672i	−0.231764	−	0.972772i	$-0.574450\pi$
$431$	10.2723	−	5.93071i	0.494799	−	0.285672i	0.726563	+	0.687100i	$0.241116\pi$
$432$	1.19612	−	3.81698i	0.0575481	−	0.183644i
$433$		−	16.9269i		−	0.813454i	−0.913550	−	0.406727i	$-0.866670\pi$
$433$		−	16.9269i		−	0.813454i	0.913550	−	0.406727i	$-0.133330\pi$
$434$		0			0
$435$		−	3.08276i		−	0.147807i
$436$	−5.47229	+	12.4664i	−0.262075	+	0.597034i
$437$	−12.2940	+	7.09795i	−0.588102	+	0.339541i
$438$	7.76030	+	11.8815i	0.370802	+	0.567721i
$439$	1.17640	−	2.03759i	0.0561467	−	0.0972489i	−0.836586	−	0.547836i	$-0.815452\pi$
$439$	1.17640	−	2.03759i	0.0561467	−	0.0972489i	0.892733	+	0.450587i	$0.148785\pi$
$440$	0.431365	+	2.59148i	0.0205645	+	0.123544i
$441$		0			0
$442$	1.68914	+	30.6913i	0.0803441	+	1.45983i
$443$	−1.38904	−	0.801965i	−0.0659955	−	0.0381025i	0.466639	−	0.884448i	$-0.345465\pi$
$443$	−1.38904	−	0.801965i	−0.0659955	−	0.0381025i	−0.532635	+	0.846345i	$0.678798\pi$
$444$	6.25965	+	8.52137i	0.297070	+	0.404406i
$445$	−2.28670	−	3.96069i	−0.108400	−	0.187755i
$446$	−3.09059	−	1.56454i	−0.146344	−	0.0740833i
$447$	−6.47939			−0.306465
$448$		0			0
$449$	1.35208			0.0638086			0.0319043	−	0.999491i	$-0.489843\pi$
$449$	1.35208			0.0638086			0.0319043	+	0.999491i	$0.489843\pi$
$450$	6.06564	+	3.07060i	0.285937	+	0.144749i
$451$	7.21350	+	12.4942i	0.339670	+	0.588327i
$452$	16.1512	+	21.9869i	0.759690	+	1.03418i
$453$	−6.72827	−	3.88457i	−0.316122	−	0.182513i
$454$	1.80919	+	32.8726i	0.0849095	+	1.54279i
$455$		0			0
$456$	−1.38203	−	8.30271i	−0.0647195	−	0.388810i
$457$	−11.0734	+	19.1797i	−0.517992	+	0.897189i	0.481789	+	0.876287i	$0.339987\pi$
$457$	−11.0734	+	19.1797i	−0.517992	+	0.897189i	−0.999782	+	0.0209017i	$0.993346\pi$
$458$	9.05345	+	13.8614i	0.423040	+	0.647702i
$459$	−4.89158	+	2.82415i	−0.228319	+	0.131820i
$460$	1.68335	−	3.83484i	0.0784864	−	0.178800i
$461$			30.7842i			1.43376i	0.697195	+	0.716882i	$0.254431\pi$
$461$			30.7842i			1.43376i	−0.697195	+	0.716882i	$0.745569\pi$
$462$		0			0
$463$		−	13.8120i		−	0.641897i	−0.947097	−	0.320948i	$-0.895998\pi$
$463$		−	13.8120i		−	0.641897i	0.947097	−	0.320948i	$-0.104002\pi$
$464$	−8.40014	+	26.8060i	−0.389967	+	1.24444i
$465$	−2.82274	+	1.62971i	−0.130901	+	0.0755759i
$466$	9.67183	−	6.31707i	0.448039	−	0.292632i
$467$	8.51330	−	14.7455i	0.393949	−	0.682339i	−0.599018	−	0.800736i	$-0.704442\pi$
$467$	8.51330	−	14.7455i	0.393949	−	0.682339i	0.992966	+	0.118397i	$0.0377754\pi$
$468$	−0.844569	−	7.64957i	−0.0390402	−	0.353602i
$469$		0			0
$470$	1.04701	−	0.0576236i	0.0482949	−	0.00265798i
$471$	−7.32996	−	4.23195i	−0.337747	−	0.194998i
$472$	−17.7304	+	14.5901i	−0.816107	+	0.671564i
$473$	−4.64082	−	8.03814i	−0.213385	−	0.369594i
$474$	9.95378	−	19.6626i	0.457192	−	0.903135i
$475$	14.3058			0.656395
$476$		0			0
$477$	10.7120			0.490468
$478$	11.6240	−	22.9619i	0.531668	−	1.05025i
$479$	15.8903	+	27.5227i	0.726045	+	1.25755i	0.958543	+	0.284950i	$0.0919769\pi$
$479$	15.8903	+	27.5227i	0.726045	+	1.25755i	−0.232498	+	0.972597i	$0.574690\pi$
$480$	1.77871	+	1.73269i	0.0811865	+	0.0790859i
$481$	17.6179	+	10.1717i	0.803306	+	0.463789i
$482$	−40.8299	+	2.24713i	−1.85975	+	0.102354i
$483$		0			0
$484$	−12.9665	+	1.43160i	−0.589386	+	0.0650726i
$485$	−0.488575	+	0.846237i	−0.0221851	+	0.0384257i
$486$	1.18404	−	0.773342i	0.0537090	−	0.0350795i
$487$	−4.99690	+	2.88496i	−0.226431	+	0.130730i	−0.608925	−	0.793228i	$-0.708399\pi$
$487$	−4.99690	+	2.88496i	−0.226431	+	0.130730i	0.382493	+	0.923958i	$0.375065\pi$
$488$	6.14233	−	16.3853i	0.278050	−	0.741727i
$489$		−	6.95459i		−	0.314497i
$490$		0			0
$491$		−	22.6443i		−	1.02192i	−0.859603	−	0.510962i	$-0.829289\pi$
$491$		−	22.6443i		−	1.02192i	0.859603	−	0.510962i	$-0.170711\pi$
$492$	12.4862	+	5.48099i	0.562924	+	0.247102i
$493$	34.3528	−	19.8336i	1.54717	−	0.893261i
$494$	−8.85563	−	13.5585i	−0.398434	−	0.610028i
$495$	−0.464416	+	0.804393i	−0.0208740	+	0.0361548i
$496$	28.9858	−	6.47946i	1.30150	−	0.290936i
$497$		0			0
$498$	0.427160	+	7.76141i	0.0191415	+	0.347797i
$499$	−16.8383	−	9.72159i	−0.753785	−	0.435198i	0.0732749	−	0.997312i	$-0.476655\pi$
$499$	−16.8383	−	9.72159i	−0.753785	−	0.435198i	−0.827060	+	0.562114i	$0.809988\pi$
$500$	−6.93907	+	5.09732i	−0.310325	+	0.227959i
$501$	−4.06011	−	7.03231i	−0.181392	−	0.314180i
$502$	25.6875	+	13.0037i	1.14649	+	0.580385i
$503$	11.7570			0.524217			0.262108	−	0.965038i	$-0.415582\pi$
$503$	11.7570			0.524217			0.262108	+	0.965038i	$0.415582\pi$
$504$		0			0
$505$	−0.337057			−0.0149989
$506$	−12.7361	−	6.44740i	−0.566191	−	0.286622i
$507$	−0.903656	−	1.56518i	−0.0401328	−	0.0695120i
$508$	5.67232	−	4.16679i	0.251669	−	0.184871i
$509$	17.4476	+	10.0734i	0.773350	+	0.446494i	0.834068	−	0.551661i	$-0.186006\pi$
$509$	17.4476	+	10.0734i	0.773350	+	0.446494i	−0.0607186	+	0.998155i	$0.519339\pi$
$510$	−0.192688	−	3.50109i	−0.00853235	−	0.155031i
$511$		0			0
$512$	−10.7453	−	19.9133i	−0.474881	−	0.880050i
$513$	1.48792	−	2.57715i	0.0656933	−	0.113784i
$514$	−16.4621	−	25.2045i	−0.726112	−	1.11172i
$515$	3.28405	−	1.89605i	0.144713	−	0.0835499i
$516$	−8.03305	−	3.52620i	−0.353635	−	0.155232i
$517$		−	3.57417i		−	0.157192i
$518$		0			0
$519$			1.41635i			0.0621710i
$520$	4.47360	+	1.67701i	0.196180	+	0.0735419i
$521$	31.0965	−	17.9536i	1.36236	−	0.786559i	0.372423	−	0.928063i	$-0.378527\pi$
$521$	31.0965	−	17.9536i	1.36236	−	0.786559i	0.989938	+	0.141504i	$0.0451937\pi$
$522$	−8.31531	+	5.43106i	−0.363951	+	0.237711i
$523$	22.6480	−	39.2276i	0.990330	−	1.71530i	0.375017	−	0.927018i	$-0.377637\pi$
$523$	22.6480	−	39.2276i	0.990330	−	1.71530i	0.615312	−	0.788283i	$-0.289030\pi$
$524$	38.9964	−	4.30548i	1.70356	−	0.188086i
$525$		0			0
$526$	−28.4951	+	1.56827i	−1.24245	+	0.0683799i
$527$	−36.3213	−	20.9701i	−1.58218	−	0.913473i
$528$	6.23018	−	5.72909i	0.271134	−	0.249327i
$529$	−0.121725	−	0.210835i	−0.00529241	−	0.00916672i
$530$	−3.00343	+	5.93295i	−0.130461	+	0.257711i
$531$	−8.11818			−0.352299
$532$		0			0
$533$	26.2364			1.13642
$534$	−6.65478	+	13.1458i	−0.287980	+	0.568874i
$535$	0.558433	+	0.967234i	0.0241432	+	0.0418172i
$536$	14.1091	+	17.1459i	0.609422	+	0.740590i
$537$	9.29401	+	5.36590i	0.401066	+	0.231556i
$538$	−23.1150	+	1.27217i	−0.996558	+	0.0548470i
$539$		0			0
$540$	0.0963438	+	0.872621i	0.00414598	+	0.0375516i
$541$	16.9491	−	29.3568i	0.728701	−	1.26215i	−0.228732	−	0.973490i	$-0.573458\pi$
$541$	16.9491	−	29.3568i	0.728701	−	1.26215i	0.957432	−	0.288657i	$-0.0932089\pi$
$542$	−15.9299	+	10.4045i	−0.684249	+	0.446911i
$543$	1.05158	−	0.607128i	0.0451275	−	0.0260543i
$544$	−7.86452	+	30.9686i	−0.337189	+	1.32777i
$545$		−	2.98815i		−	0.127998i
$546$		0			0
$547$		−	7.83251i		−	0.334894i	−0.985881	−	0.167447i	$-0.946448\pi$
$547$		−	7.83251i		−	0.334894i	0.985881	−	0.167447i	$-0.0535523\pi$
$548$	−2.71574	+	6.18674i	−0.116011	+	0.264284i
$549$	5.35787	−	3.09337i	0.228668	−	0.132022i
$550$	7.86656	+	12.0442i	0.335431	+	0.513567i
$551$	−10.4494	+	18.0990i	−0.445161	+	0.771042i
$552$	−13.3096	+	2.21544i	−0.566492	+	0.0942956i
$553$		0			0
$554$	−0.218172	−	3.96414i	−0.00926925	−	0.168420i
$555$	−2.00975	−	1.16033i	−0.0853092	−	0.0492533i
$556$	−19.4752	−	26.5119i	−0.825932	−	1.12436i
$557$	−7.69701	−	13.3316i	−0.326133	−	0.564879i	0.655608	−	0.755101i	$-0.272412\pi$
$557$	−7.69701	−	13.3316i	−0.326133	−	0.564879i	−0.981741	+	0.190223i	$0.939079\pi$
$558$	9.36887	+	4.74278i	0.396616	+	0.200778i
$559$	−16.8792			−0.713914
$560$		0			0
$561$	−11.9517			−0.504600
$562$	−32.1118	−	16.2559i	−1.35455	−	0.685714i
$563$	−8.22052	−	14.2384i	−0.346453	−	0.600075i	0.639163	−	0.769071i	$-0.279281\pi$
$563$	−8.22052	−	14.2384i	−0.346453	−	0.600075i	−0.985617	+	0.168996i	$0.945947\pi$
$564$	−2.00000	−	2.72263i	−0.0842152	−	0.114644i
$565$	−5.18559	−	2.99390i	−0.218159	−	0.125954i
$566$	0.368333	+	6.69252i	0.0154822	+	0.281308i
$567$		0			0
$568$	3.26385	−	0.543286i	0.136948	−	0.0227958i
$569$	18.6146	−	32.2415i	0.780366	−	1.35163i	−0.151363	−	0.988478i	$-0.548366\pi$
$569$	18.6146	−	32.2415i	0.780366	−	1.35163i	0.931729	−	0.363155i	$-0.118300\pi$
$570$	1.01020	+	1.54668i	0.0423127	+	0.0647835i
$571$	17.9660	−	10.3727i	0.751854	−	0.434083i	−0.0745095	−	0.997220i	$-0.523739\pi$
$571$	17.9660	−	10.3727i	0.751854	−	0.434083i	0.826363	+	0.563137i	$0.190406\pi$
$572$	6.54549	−	14.9113i	0.273681	−	0.623473i
$573$			6.55261i			0.273739i
$574$		0			0
$575$		−	22.9327i		−	0.956361i
$576$	1.54003	−	7.85037i	0.0641679	−	0.327099i
$577$	13.3550	−	7.71054i	0.555978	−	0.320994i	−0.195552	−	0.980693i	$-0.562650\pi$
$577$	13.3550	−	7.71054i	0.555978	−	0.320994i	0.751530	+	0.659699i	$0.229316\pi$
$578$	17.6461	−	11.5254i	0.733982	−	0.479393i
$579$	−1.61818	+	2.80276i	−0.0672491	+	0.116479i
$580$	−0.676608	−	6.12829i	−0.0280946	−	0.254463i
$581$		0			0
$582$	3.14335	−	0.172999i	0.130296	−	0.00717104i
$583$	19.6296	+	11.3332i	0.812975	+	0.469371i
$584$	18.0346	+	21.9163i	0.746279	+	0.906902i
$585$	0.844569	+	1.46284i	0.0349186	+	0.0604808i
$586$	2.06195	−	4.07316i	0.0851783	−	0.168261i
$587$	−34.0410			−1.40502			−0.702512	−	0.711672i	$-0.747938\pi$
$587$	−34.0410			−1.40502			−0.702512	+	0.711672i	$0.747938\pi$
$588$		0			0
$589$	22.0965			0.910469
$590$	2.27618	−	4.49634i	0.0937086	−	0.185111i
$591$	−9.62772	−	16.6757i	−0.396032	−	0.685947i
$592$	14.3140	+	15.5659i	0.588300	+	0.639756i
$593$	−27.5697	−	15.9173i	−1.13215	−	0.653647i	−0.187675	−	0.982231i	$-0.560095\pi$
$593$	−27.5697	−	15.9173i	−1.13215	−	0.653647i	−0.944475	+	0.328584i	$0.893429\pi$
$594$	2.98792	−	0.164445i	0.122596	−	0.00674724i
$595$		0			0
$596$	−12.8805	+	1.42210i	−0.527606	+	0.0582516i
$597$	4.31086	−	7.46663i	0.176432	−	0.305589i
$598$	−21.7348	+	14.1959i	−0.888804	+	0.580514i
$599$	−18.0000	+	10.3923i	−0.735460	+	0.424618i	−0.820416	−	0.571767i	$-0.806258\pi$
$599$	−18.0000	+	10.3923i	−0.735460	+	0.424618i	0.0849563	+	0.996385i	$0.472925\pi$
$600$	12.7319	+	4.77281i	0.519779	+	0.194849i
$601$			15.8614i			0.646999i	0.946228	+	0.323499i	$0.104859\pi$
$601$			15.8614i			0.646999i	−0.946228	+	0.323499i	$0.895141\pi$
$602$		0			0
$603$			7.85056i			0.319699i
$604$	−14.2279	−	6.24549i	−0.578923	−	0.254125i
$605$	2.47960	−	1.43160i	0.100810	−	0.0582027i
$606$	0.593811	+	0.909163i	0.0241219	+	0.0369322i
$607$	21.7151	−	37.6116i	0.881388	−	1.52661i	0.0315900	−	0.999501i	$-0.489943\pi$
$607$	21.7151	−	37.6116i	0.881388	−	1.52661i	0.849798	−	0.527108i	$-0.176724\pi$
$608$	−4.56965	−	16.2018i	−0.185324	−	0.657070i
$609$		0			0
$610$	0.211056	+	3.83484i	0.00854539	+	0.155268i
$611$	−5.62903	−	3.24992i	−0.227726	−	0.131478i
$612$	−9.10422	+	6.68780i	−0.368016	+	0.270338i
$613$	−7.76030	−	13.4412i	−0.313436	−	0.542887i	0.665668	−	0.746248i	$-0.268147\pi$
$613$	−7.76030	−	13.4412i	−0.313436	−	0.542887i	−0.979104	+	0.203361i	$0.934813\pi$
$614$	−6.88315	−	3.48445i	−0.277781	−	0.140621i
$615$	−2.99290			−0.120685
$616$		0			0
$617$	−19.8053			−0.797330			−0.398665	−	0.917097i	$-0.630526\pi$
$617$	−19.8053			−0.797330			−0.398665	+	0.917097i	$0.630526\pi$
$618$	−10.9000	−	5.51789i	−0.438462	−	0.221962i
$619$	8.15665	+	14.1277i	0.327844	+	0.567842i	0.982084	−	0.188445i	$-0.0603448\pi$
$619$	8.15665	+	14.1277i	0.327844	+	0.567842i	−0.654240	+	0.756287i	$0.727011\pi$
$620$	−5.25369	+	3.85927i	−0.210993	+	0.154992i
$621$	−4.13127	−	2.38519i	−0.165782	−	0.0957144i
$622$	−2.37228	−	43.1038i	−0.0951197	−	1.72830i
$623$		0			0
$624$	−3.35787	−	15.0214i	−0.134422	−	0.601336i
$625$	−11.0734	+	19.1797i	−0.442936	+	0.767188i
$626$	14.5639	+	22.2983i	0.582090	+	0.891218i
$627$	5.45320	−	3.14840i	0.217780	−	0.125735i
$628$	−15.5002	−	6.80400i	−0.618526	−	0.271509i
$629$		−	29.8609i		−	1.19063i
$630$		0			0
$631$		−	27.3095i		−	1.08717i	−0.839353	−	0.543587i	$-0.817066\pi$
$631$		−	27.3095i		−	1.08717i	0.839353	−	0.543587i	$-0.182934\pi$
$632$	15.4718	−	41.2724i	0.615433	−	1.64173i
$633$	−5.28091	+	3.04894i	−0.209897	+	0.121184i
$634$	−20.3242	+	13.2746i	−0.807177	+	0.527200i
$635$	−0.772384	+	1.33781i	−0.0306511	+	0.0530893i
$636$	21.2946	−	2.35108i	0.844385	−	0.0932263i
$637$		0			0
$638$	−20.9837	+	1.15487i	−0.830753	+	0.0457217i
$639$	1.01310	+	0.584912i	0.0400775	+	0.0231388i
$640$	3.91622	+	3.05405i	0.154802	+	0.120722i
$641$	−4.89533	−	8.47896i	−0.193354	−	0.334899i	0.753006	−	0.658014i	$-0.228603\pi$
$641$	−4.89533	−	8.47896i	−0.193354	−	0.334899i	−0.946360	+	0.323115i	$0.895270\pi$
$642$	1.62515	−	3.21032i	0.0641397	−	0.126701i
$643$	7.26458			0.286487			0.143244	−	0.989687i	$-0.454247\pi$
$643$	7.26458			0.286487			0.143244	+	0.989687i	$0.454247\pi$
$644$		0			0
$645$	1.92549			0.0758160
$646$	−10.7361	+	21.2081i	−0.422408	+	0.834422i
$647$	−23.0419	−	39.9098i	−0.905872	−	1.56902i	−0.819742	−	0.572733i	$-0.805883\pi$
$647$	−23.0419	−	39.9098i	−0.905872	−	1.56902i	−0.0861302	−	0.996284i	$-0.527450\pi$
$648$	2.18404	−	1.79722i	0.0857971	−	0.0706013i
$649$	−14.8765	−	8.58893i	−0.583952	−	0.337145i
$650$	26.1215	−	1.43764i	1.02457	−	0.0563887i
$651$		0			0
$652$	−1.52640	−	13.8252i	−0.0597784	−	0.541435i
$653$	3.38990	−	5.87149i	0.132657	−	0.229769i	−0.792043	−	0.610465i	$-0.790982\pi$
$653$	3.38990	−	5.87149i	0.132657	−	0.229769i	0.924700	+	0.380696i	$0.124316\pi$
$654$	−8.06011	+	5.26438i	−0.315175	+	0.205854i
$655$	−7.45732	+	4.30548i	−0.291381	+	0.168229i
$656$	26.0246	+	8.15527i	1.01609	+	0.318410i
$657$			10.0348i			0.391493i
$658$		0			0
$659$			29.3184i			1.14208i	0.820921	+	0.571041i	$0.193460\pi$
$659$			29.3184i			1.14208i	−0.820921	+	0.571041i	$0.806540\pi$
$660$	−0.746674	+	1.70100i	−0.0290643	+	0.0662113i
$661$	−26.4813	+	15.2890i	−1.03000	+	0.594674i	−0.916986	−	0.398919i	$-0.869385\pi$
$661$	−26.4813	+	15.2890i	−1.03000	+	0.594674i	−0.113019	+	0.993593i	$0.536052\pi$
$662$	16.6167	+	25.4412i	0.645825	+	0.988799i
$663$	−10.8674	+	18.8229i	−0.422056	+	0.731022i
$664$	2.55264	+	15.3353i	0.0990617	+	0.595125i
$665$		0			0
$666$	0.410860	+	7.46523i	0.0159205	+	0.289272i
$667$	29.0133	+	16.7508i	1.12340	+	0.648595i
$668$	−9.61462	−	13.0886i	−0.372001	−	0.506411i
$669$	−1.22472	−	2.12128i	−0.0473504	−	0.0820134i
$670$	−4.34812	−	2.20114i	−0.167982	−	0.0850375i
$671$	13.0910			0.505372
$672$		0			0
$673$	−6.37827			−0.245864			−0.122932	−	0.992415i	$-0.539230\pi$
$673$	−6.37827			−0.245864			−0.122932	+	0.992415i	$0.539230\pi$
$674$	7.45754	+	3.77522i	0.287254	+	0.145416i
$675$	2.40366	+	4.16325i	0.0925168	+	0.160244i
$676$	−2.13992	−	2.91312i	−0.0823048	−	0.112043i
$677$	10.8219	+	6.24801i	0.415919	+	0.240131i	0.693330	−	0.720621i	$-0.256143\pi$
$677$	10.8219	+	6.24801i	0.415919	+	0.240131i	−0.277411	+	0.960751i	$0.589476\pi$
$678$	1.06011	+	19.2619i	0.0407131	+	0.739748i
$679$		0			0
$680$	−1.15147	−	6.91760i	−0.0441569	−	0.265278i
$681$	−11.6398	+	20.1607i	−0.446038	+	0.772561i
$682$	12.1505	+	18.6033i	0.465268	+	0.712355i
$683$	39.1917	−	22.6273i	1.49963	−	0.865811i	0.499629	−	0.866240i	$-0.333470\pi$
$683$	39.1917	−	22.6273i	1.49963	−	0.865811i	1.00000		0.000428478i	$0.000136389\pi$
$684$	2.39223	−	5.44975i	0.0914693	−	0.208376i
$685$		−	1.48293i		−	0.0566600i
$686$		0			0
$687$			11.7069i			0.446647i
$688$	−16.7430	−	5.24671i	−0.638321	−	0.200029i
$689$	35.6976	−	20.6100i	1.35997	−	0.785179i
$690$	2.47939	−	1.61939i	0.0943888	−	0.0616492i
$691$	5.29654	−	9.17388i	0.201490	−	0.348991i	−0.747519	−	0.664241i	$-0.768755\pi$
$691$	5.29654	−	9.17388i	0.201490	−	0.348991i	0.949009	+	0.315250i	$0.102088\pi$
$692$	0.310863	+	2.81560i	0.0118172	+	0.107033i
$693$		0			0
$694$	−3.97584	+	0.218816i	−0.150921	+	0.00830615i
$695$	6.25279	+	3.61005i	0.237182	+	0.136937i
$696$	−15.3382	+	12.6216i	−0.581391	+	0.478420i
$697$	−19.2554	−	33.3514i	−0.729352	−	1.26327i
$698$	6.09402	−	12.0381i	0.230662	−	0.455648i
$699$	8.16853			0.308962
$700$		0			0
$701$	29.6566			1.12011			0.560057	−	0.828454i	$-0.310779\pi$
$701$	29.6566			1.12011			0.560057	+	0.828454i	$0.310779\pi$
$702$	2.45787	−	4.85526i	0.0927662	−	0.183250i
$703$	7.86620	+	13.6246i	0.296679	+	0.513863i
$704$	11.1277	−	12.7564i	0.419390	−	0.480774i
$705$	0.642129	+	0.370733i	0.0241840	+	0.0139626i
$706$	−14.0772	+	0.774757i	−0.529801	+	0.0291584i
$707$		0			0
$708$	−16.1383	+	1.78178i	−0.606514	+	0.0669636i
$709$	17.8506	−	30.9181i	0.670392	−	1.16115i	−0.307401	−	0.951580i	$-0.599459\pi$
$709$	17.8506	−	30.9181i	0.670392	−	1.16115i	0.977793	−	0.209573i	$-0.0672074\pi$
$710$	−0.608012	+	0.397117i	−0.0228183	+	0.0149036i
$711$	13.4958	−	7.79180i	0.506132	−	0.292215i
$712$	−10.3439	+	27.5934i	−0.387655	+	1.03411i
$713$		−	35.4214i		−	1.32654i
$714$		0			0
$715$			3.57417i			0.133667i
$716$	19.6535	+	8.62712i	0.734485	+	0.322411i
$717$	15.7603	−	9.09922i	0.588579	−	0.339816i
$718$	5.35787	+	8.20324i	0.199954	+	0.306142i
$719$	6.40447	−	11.0929i	0.238846	−	0.413694i	−0.721537	−	0.692376i	$-0.756564\pi$
$719$	6.40447	−	11.0929i	0.238846	−	0.413694i	0.960384	+	0.278682i	$0.0898974\pi$
$720$	0.383048	+	1.71356i	0.0142753	+	0.0638605i
$721$		0			0
$722$	0.788376	+	14.3246i	0.0293403	+	0.533107i
$723$	−25.0409	−	14.4574i	−0.931282	−	0.537676i
$724$	1.95720	−	1.43772i	0.0727387	−	0.0534325i
$725$	−16.8805	−	29.2379i	−0.626927	−	1.08587i
$726$	−8.22996	−	4.16624i	−0.305442	−	0.154624i
$727$	−19.3286			−0.716860			−0.358430	−	0.933557i	$-0.616688\pi$
$727$	−19.3286			−0.716860			−0.358430	+	0.933557i	$0.616688\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−5.55786	−	2.81355i	−0.205706	−	0.104134i
$731$	12.3880	+	21.4567i	0.458188	+	0.793604i
$732$	9.97209	−	7.32532i	0.368579	−	0.270752i
$733$	32.6407	+	18.8451i	1.20561	+	0.696061i	0.961798	−	0.273761i	$-0.0882676\pi$
$733$	32.6407	+	18.8451i	1.20561	+	0.696061i	0.243815	+	0.969822i	$0.421601\pi$
$734$	−1.39147	−	25.2828i	−0.0513602	−	0.933204i
$735$		0			0
$736$	−25.9721	+	7.32532i	−0.957344	+	0.270015i
$737$	−8.30580	+	14.3861i	−0.305948	+	0.529917i
$738$	5.27275	+	8.07291i	0.194092	+	0.297168i
$739$	−12.0072	+	6.93237i	−0.441693	+	0.255011i	−0.704315	−	0.709887i	$-0.748746\pi$
$739$	−12.0072	+	6.93237i	−0.441693	+	0.255011i	0.262623	+	0.964899i	$0.415413\pi$
$740$	−4.24990	−	1.86554i	−0.156229	−	0.0685787i
$741$		−	11.4511i		−	0.420667i
$742$		0			0
$743$			18.9927i			0.696773i	0.937351	+	0.348387i	$0.113270\pi$
$743$			18.9927i			0.696773i	−0.937351	+	0.348387i	$0.886730\pi$
$744$	19.6655	+	7.37199i	0.720973	+	0.270270i
$745$	2.46315	−	1.42210i	0.0902430	−	0.0521018i
$746$	−17.1381	+	11.1936i	−0.627471	+	0.409827i
$747$	−2.74822	+	4.76007i	−0.100552	+	0.174162i
$748$	−23.7590	+	2.62317i	−0.868715	+	0.0959125i
$749$		0			0
$750$	−6.07904	+	0.334569i	−0.221975	+	0.0122167i
$751$	25.2868	+	14.5993i	0.922728	+	0.532737i	0.884504	−	0.466532i	$-0.154497\pi$
$751$	25.2868	+	14.5993i	0.922728	+	0.532737i	0.0382233	+	0.999269i	$0.487830\pi$
$752$	−4.57341	−	4.97342i	−0.166775	−	0.181362i
$753$	10.1793	+	17.6311i	0.370954	+	0.642512i
$754$	−17.2612	+	34.0977i	−0.628617	+	1.24177i
$755$	3.41036			0.124116
$756$		0			0
$757$	−10.8022			−0.392614			−0.196307	−	0.980542i	$-0.562895\pi$
$757$	−10.8022			−0.392614			−0.196307	+	0.980542i	$0.562895\pi$
$758$	−13.7947	+	27.2499i	−0.501045	+	0.989762i
$759$	−5.04701	−	8.74167i	−0.183195	−	0.317303i
$760$	2.34767	+	2.85296i	0.0851589	+	0.103488i
$761$	0.203165	+	0.117298i	0.00736474	+	0.00425204i	0.503678	−	0.863892i	$-0.331980\pi$
$761$	0.203165	+	0.117298i	0.00736474	+	0.00425204i	−0.496313	+	0.868144i	$0.665313\pi$
$762$	4.96929	−	0.273492i	0.180018	−	0.00990758i
$763$		0			0
$764$	1.43817	+	13.0261i	0.0520313	+	0.471267i
$765$	1.23970	−	2.14722i	0.0448213	−	0.0776328i
$766$	0.753448	−	0.492107i	0.0272232	−	0.0177806i
$767$	−27.0537	+	15.6195i	−0.976854	+	0.563987i
$768$	1.33845	−	15.9439i	0.0482971	−	0.575327i
$769$			34.8540i			1.25687i	0.777863	+	0.628434i	$0.216304\pi$
$769$			34.8540i			1.25687i	−0.777863	+	0.628434i	$0.783696\pi$
$770$		0			0
$771$		−	21.2869i		−	0.766631i
$772$	−2.60165	+	5.92683i	−0.0936355	+	0.213311i
$773$	−17.0362	+	9.83583i	−0.612748	+	0.353770i	−0.774040	−	0.633137i	$-0.781767\pi$
$773$	−17.0362	+	9.83583i	−0.612748	+	0.353770i	0.161292	+	0.986907i	$0.448434\pi$
$774$	−3.39223	−	5.19372i	−0.121931	−	0.186685i
$775$	−17.8478	+	30.9133i	−0.641113	+	1.11044i
$776$	6.21076	−	1.03381i	0.222953	−	0.0371118i
$777$		0			0
$778$	0.0791996	+	1.43904i	0.00283944	+	0.0515920i
$779$	17.5714	+	10.1448i	0.629560	+	0.363476i
$780$	2.00000	+	2.72263i	0.0716115	+	0.0974860i
$781$	1.23766	+	2.14369i	0.0442870	+	0.0767073i
$782$	33.9974	+	17.2104i	1.21574	+	0.615444i
$783$	−7.02285			−0.250976
$784$		0			0
$785$	3.71533			0.132606
$786$	24.7514	+	12.5298i	0.882852	+	0.446925i
$787$	19.4781	+	33.7370i	0.694319	+	1.20260i	0.970410	+	0.241464i	$0.0776275\pi$
$787$	19.4781	+	33.7370i	0.694319	+	1.20260i	−0.276091	+	0.961131i	$0.589039\pi$
$788$	−22.7991	−	31.0369i	−0.812186	−	1.10564i
$789$	−17.4760	−	10.0898i	−0.622164	−	0.359206i
$790$	0.531622	+	9.65946i	0.0189143	+	0.343668i
$791$		0			0
$792$	5.90366	−	0.982694i	0.209777	−	0.0349185i
$793$	11.9034	−	20.6172i	0.422701	−	0.732139i
$794$	−23.0419	−	35.2787i	−0.817728	−	1.25199i
$795$	−4.07218	+	2.35108i	−0.144426	+	0.0833841i
$796$	6.93087	−	15.7892i	0.245658	−	0.559634i
$797$			20.4557i			0.724579i	0.932066	+	0.362289i	$0.118005\pi$
$797$			20.4557i			0.724579i	−0.932066	+	0.362289i	$0.881995\pi$
$798$		0			0
$799$			9.54077i			0.337528i
$800$	26.3576	+	6.69355i	0.931883	+	0.236653i
$801$	−9.02285	+	5.20934i	−0.318807	+	0.184063i
$802$	8.03991	−	5.25119i	0.283899	−	0.185426i
$803$	−10.6167	+	18.3886i	−0.374654	+	0.648919i
$804$	1.72305	+	15.6063i	0.0607672	+	0.550391i
$805$		0			0
$806$	40.3468	−	2.22055i	1.42116	−	0.0782154i
$807$	−14.1764	−	8.18475i	−0.499033	−	0.288117i
$808$	1.37999	+	1.67701i	0.0485480	+	0.0589972i
$809$	24.4650	+	42.3746i	0.860143	+	1.48981i	0.871790	+	0.489879i	$0.162959\pi$
$809$	24.4650	+	42.3746i	0.860143	+	1.48981i	−0.0116472	+	0.999932i	$0.503708\pi$
$810$	−0.280380	+	0.553861i	−0.00985155	+	0.0194607i
$811$	51.9424			1.82394			0.911972	−	0.410253i	$-0.134560\pi$
$811$	51.9424			1.82394			0.911972	+	0.410253i	$0.134560\pi$
$812$		0			0
$813$	−13.4539			−0.471850
$814$	−7.14523	+	14.1146i	−0.250440	+	0.494718i
$815$	1.52640	+	2.64380i	0.0534674	+	0.0926083i
$816$	−16.6306	+	15.2930i	−0.582188	+	0.535363i
$817$	−11.3046	−	6.52670i	−0.395497	−	0.228340i
$818$	−5.24335	+	0.288575i	−0.183329	+	0.0100898i
$819$		0			0
$820$	−5.94965	+	0.656884i	−0.207771	+	0.0229394i
$821$	−15.7322	+	27.2490i	−0.549059	+	0.950998i	0.449281	+	0.893391i	$0.351680\pi$
$821$	−15.7322	+	27.2490i	−0.549059	+	0.950998i	−0.998339	+	0.0576069i	$0.981653\pi$
$822$	−4.00000	+	2.61256i	−0.139516	+	0.0911236i
$823$	−35.9504	+	20.7560i	−1.25315	+	0.723507i	−0.971734	−	0.236078i	$-0.924138\pi$
$823$	−35.9504	+	20.7560i	−1.25315	+	0.723507i	−0.281417	+	0.959586i	$0.590804\pi$
$824$	−22.8794	−	8.57678i	−0.797042	−	0.298786i
$825$			10.1722i			0.354149i
$826$		0			0
$827$			38.6850i			1.34521i	0.740003	+	0.672604i	$0.234824\pi$
$827$			38.6850i			1.34521i	−0.740003	+	0.672604i	$0.765176\pi$
$828$	−8.73615	−	3.83484i	−0.303602	−	0.133270i
$829$	−8.94508	+	5.16444i	−0.310675	+	0.179369i	−0.647229	−	0.762296i	$-0.724072\pi$
$829$	−8.94508	+	5.16444i	−0.310675	+	0.179369i	0.336553	+	0.941664i	$0.390739\pi$
$830$	−1.86587	−	2.85676i	−0.0647652	−	0.0991597i
$831$	1.40366	−	2.43120i	0.0486923	−	0.0843375i
$832$	−9.97209	−	29.1243i	−0.345720	−	1.00970i
$833$		0			0
$834$	−1.27828	−	23.2260i	−0.0442631	−	0.804251i
$835$	3.08692	+	1.78223i	0.106827	+	0.0616767i
$836$	10.1495	−	7.45565i	0.351028	−	0.257859i
$837$	3.71264	+	6.43048i	0.128328	+	0.222270i
$838$	−26.1287	−	13.2271i	−0.902599	−	0.456921i
$839$	10.4794			0.361789			0.180894	−	0.983503i	$-0.442101\pi$
$839$	10.4794			0.361789			0.180894	+	0.983503i	$0.442101\pi$
$840$		0			0
$841$	20.3204			0.700704
$842$	19.7564	+	10.0012i	0.680849	+	0.344665i
$843$	−12.7251	−	22.0405i	−0.438275	−	0.759115i
$844$	−9.82885	+	7.22010i	−0.338323	+	0.248526i
$845$	0.687054	+	0.396671i	0.0236354	+	0.0136459i
$846$	−0.131272	−	2.38519i	−0.00451324	−	0.0820046i
$847$		0			0
$848$	41.8159	−	9.34751i	1.43596	−	0.320995i
$849$	−2.36975	+	4.10452i	−0.0813295	+	0.140867i
$850$	−20.9987	−	32.1503i	−0.720249	−	1.10275i
$851$	21.8408	−	12.6098i	0.748693	−	0.432258i
$852$	2.14233	+	0.940403i	0.0733952	+	0.0322177i
$853$			25.5157i			0.873642i	0.899548	+	0.436821i	$0.143896\pi$
$853$			25.5157i			0.873642i	−0.899548	+	0.436821i	$0.856104\pi$
$854$		0			0
$855$			1.30628i			0.0446739i
$856$	2.52607	−	6.73855i	0.0863394	−	0.230319i
$857$	9.99828	−	5.77251i	0.341535	−	0.197185i	−0.319416	−	0.947615i	$-0.603487\pi$
$857$	9.99828	−	5.77251i	0.341535	−	0.197185i	0.660951	+	0.750429i	$0.270153\pi$
$858$	9.64082	−	6.29681i	0.329132	−	0.214970i
$859$	−16.4552	+	28.5013i	−0.561445	+	0.972452i	0.435925	+	0.899983i	$0.356421\pi$
$859$	−16.4552	+	28.5013i	−0.561445	+	0.972452i	−0.997371	+	0.0724689i	$0.976912\pi$
$860$	3.82772	−	0.422608i	0.130524	−	0.0144108i
$861$		0			0
$862$	16.7492	−	0.921819i	0.570481	−	0.0313973i
$863$	−49.6075	−	28.6409i	−1.68866	−	0.974948i	−0.955546	−	0.294842i	$-0.904733\pi$
$863$	−49.6075	−	28.6409i	−1.68866	−	0.974948i	−0.733114	−	0.680106i	$-0.761934\pi$
$864$	3.94724	−	4.05208i	0.134288	−	0.137854i
$865$	−0.310863	−	0.538430i	−0.0105696	−	0.0183072i
$866$	10.8118	−	21.3575i	0.367399	−	0.725758i
$867$	14.9034			0.506145
$868$		0			0
$869$	32.9745			1.11858
$870$	1.96907	−	3.88968i	0.0667576	−	0.131873i
$871$	15.1046	+	26.1619i	0.511799	+	0.886462i
$872$	−14.8674	+	12.2342i	−0.503474	+	0.414303i
$873$	1.92782	+	1.11302i	0.0652467	+	0.0376702i
$874$	−20.0457	+	1.10324i	−0.678056	+	0.0373178i
$875$		0			0
$876$	2.20244	+	19.9483i	0.0744135	+	0.673991i
$877$	−17.0215	+	29.4822i	−0.574777	+	0.995542i	0.421289	+	0.906926i	$0.361578\pi$
$877$	−17.0215	+	29.4822i	−0.574777	+	0.995542i	−0.996066	+	0.0886159i	$0.971756\pi$
$878$	2.78581	−	1.81952i	0.0940165	−	0.0614060i
$879$	2.79568	−	1.61409i	0.0942960	−	0.0544418i
$880$	−1.11099	+	3.54533i	−0.0374515	+	0.119513i
$881$		−	23.4638i		−	0.790514i	−0.918571	−	0.395257i	$-0.870656\pi$
$881$		−	23.4638i		−	0.790514i	0.918571	−	0.395257i	$-0.129344\pi$
$882$		0			0
$883$		−	8.14468i		−	0.274090i	−0.990565	−	0.137045i	$-0.956239\pi$
$883$		−	8.14468i		−	0.274090i	0.990565	−	0.137045i	$-0.0437606\pi$
$884$	−17.4723	+	39.8037i	−0.587657	+	1.33874i
$885$	3.08614	−	1.78178i	0.103740	−	0.0598940i
$886$	−1.24039	−	1.89911i	−0.0416716	−	0.0638019i
$887$	−14.6109	+	25.3068i	−0.490585	+	0.849718i	−0.999941	−	0.0108376i	$-0.996550\pi$
$887$	−14.6109	+	25.3068i	−0.490585	+	0.849718i	0.509356	+	0.860556i	$0.329884\pi$
$888$	2.45523	+	14.7501i	0.0823922	+	0.494981i
$889$		0			0
$890$	−0.355425	−	6.45800i	−0.0119139	−	0.216473i
$891$	1.83249	+	1.05799i	0.0613907	+	0.0354439i
$892$	−2.90023	−	3.94813i	−0.0971068	−	0.132193i
$893$	−2.51330	−	4.35317i	−0.0841044	−	0.145673i
$894$	−8.17539	−	4.13861i	−0.273426	−	0.138416i
$895$	−4.71085			−0.157466
$896$		0			0
$897$	−18.3566			−0.612908
$898$	1.70599	+	0.863620i	0.0569296	+	0.0288194i
$899$	−26.0733	−	45.1603i	−0.869594	−	1.50618i
$900$	5.69203	+	7.74866i	0.189734	+	0.258289i
$901$	−52.3985	−	30.2523i	−1.74565	−	1.00785i
$902$	1.12120	+	20.3720i	0.0373320	+	0.678314i
$903$		0			0
$904$	6.33502	+	38.0584i	0.210700	+	1.26580i
$905$	−0.266506	+	0.461602i	−0.00885896	+	0.0153442i
$906$	−6.00820	−	9.19894i	−0.199609	−	0.305614i
$907$	−48.5997	+	28.0591i	−1.61373	+	0.931686i	−0.625231	+	0.780440i	$0.714995\pi$
$907$	−48.5997	+	28.0591i	−1.61373	+	0.931686i	−0.988496	+	0.151246i	$0.951671\pi$
$908$	−18.7141	+	42.6326i	−0.621049	+	1.41481i
$909$			0.767851i			0.0254680i
$910$		0			0
$911$		−	43.1536i		−	1.42974i	−0.699256	−	0.714871i	$-0.746485\pi$
$911$		−	43.1536i		−	1.42974i	0.699256	−	0.714871i	$-0.253515\pi$
$912$	3.55945	−	11.3587i	0.117865	−	0.376125i
$913$	−10.0722	+	5.81518i	−0.333341	+	0.192454i
$914$	−26.2226	+	17.1271i	−0.867368	+	0.566513i
$915$	−1.35787	+	2.35190i	−0.0448898	+	0.0777515i
$916$	2.56945	+	23.2724i	0.0848969	+	0.768943i
$917$		0			0
$918$	−7.97584	+	0.438962i	−0.263242	+	0.0144879i
$919$	33.3617	+	19.2614i	1.10050	+	0.635375i	0.936353	−	0.351060i	$-0.114179\pi$
$919$	33.3617	+	19.2614i	1.10050	+	0.635375i	0.164149	+	0.986435i	$0.447512\pi$
$920$	4.57341	−	3.76340i	0.150781	−	0.124076i
$921$	−2.72762	−	4.72437i	−0.0898780	−	0.155673i
$922$	−19.6629	+	38.8420i	−0.647565	+	1.27919i
$923$	4.50151			0.148169
$924$		0			0
$925$	−25.4148			−0.835635
$926$	8.82219	−	17.4273i	0.289915	−	0.572696i
$927$	−4.31939	−	7.48141i	−0.141867	−	0.245722i
$928$	−27.7208	+	28.4571i	−0.909981	+	0.934151i
$929$	41.3034	+	23.8465i	1.35512	+	0.782379i	0.988961	−	0.148173i	$-0.0473394\pi$
$929$	41.3034	+	23.8465i	1.35512	+	0.782379i	0.366159	+	0.930552i	$0.380673\pi$
$930$	−4.60255	+	0.253308i	−0.150923	+	0.00830629i
$931$		0			0
$932$	16.2384	−	1.79284i	0.531906	−	0.0587263i
$933$	15.2625	−	26.4355i	0.499673	−	0.865460i
$934$	20.1601	−	13.1674i	0.659659	−	0.430850i
$935$	4.54346	−	2.62317i	0.148587	−	0.0857867i
$936$	3.82041	−	10.1913i	0.124874	−	0.333114i
$937$		−	6.18932i		−	0.202196i	−0.994876	−	0.101098i	$-0.967764\pi$
$937$		−	6.18932i		−	0.202196i	0.994876	−	0.101098i	$-0.0322356\pi$
$938$		0			0
$939$			18.8324i			0.614573i
$940$	1.35787	+	0.596054i	0.0442889	+	0.0194411i
$941$	6.33052	−	3.65493i	0.206369	−	0.119147i	−0.393254	−	0.919430i	$-0.628651\pi$
$941$	6.33052	−	3.65493i	0.206369	−	0.119147i	0.599623	+	0.800283i	$0.295317\pi$
$942$	−6.54549	−	10.0216i	−0.213264	−	0.326520i
$943$	16.2625	−	28.1676i	0.529581	−	0.917262i
$944$	−31.6906	+	7.08409i	−1.03144	+	0.230568i
$945$		0			0
$946$	−0.721329	−	13.1064i	−0.0234524	−	0.426125i
$947$	13.1805	+	7.60978i	0.428309	+	0.247285i	0.698626	−	0.715487i	$-0.253795\pi$
$947$	13.1805	+	7.60978i	0.428309	+	0.247285i	−0.270317	+	0.962771i	$0.587128\pi$
$948$	25.1184	−	18.4516i	0.815808	−	0.599279i
$949$	19.3070	+	33.4407i	0.626732	+	1.08553i
$950$	18.0504	+	9.13761i	0.585631	+	0.296463i
$951$	−17.1652			−0.556619
$952$		0			0
$953$	17.5899			0.569792			0.284896	−	0.958558i	$-0.408041\pi$
$953$	17.5899			0.569792			0.284896	+	0.958558i	$0.408041\pi$
$954$	13.5159	+	6.84212i	0.437592	+	0.221522i
$955$	−1.43817	−	2.49099i	−0.0465382	−	0.0806066i
$956$	29.3331	−	21.5476i	0.948701	−	0.696899i
$957$	−12.8693	−	7.43009i	−0.416005	−	0.240181i
$958$	2.46985	+	44.8765i	0.0797971	+	1.44990i
$959$		0			0
$960$	1.13756	+	3.32234i	0.0367146	+	0.107228i
$961$	−12.0674	+	20.9014i	−0.389271	+	0.674238i
$962$	15.7324	+	24.0873i	0.507233	+	0.776606i
$963$	2.20346	−	1.27217i	0.0710054	−	0.0409950i
$964$	−52.9525	−	23.2441i	−1.70548	−	0.748643i
$965$		−	1.42063i		−	0.0457318i
$966$		0			0
$967$			15.0905i			0.485279i	0.970117	+	0.242640i	$0.0780132\pi$
$967$			15.0905i			0.485279i	−0.970117	+	0.242640i	$0.921987\pi$
$968$	−17.2749	−	6.47583i	−0.555237	−	0.208141i
$969$	−14.5566	+	8.40423i	−0.467624	+	0.269983i
$970$	−1.15698	+	0.755672i	−0.0371485	+	0.0242632i
$971$	−22.4660	+	38.9123i	−0.720968	+	1.24875i	0.239644	+	0.970861i	$0.422969\pi$
$971$	−22.4660	+	38.9123i	−0.720968	+	1.24875i	−0.960612	+	0.277893i	$0.910364\pi$
$972$	1.98792	−	0.219481i	0.0637626	−	0.00703985i
$973$		0			0
$974$	−8.14757	+	0.448413i	−0.261065	+	0.0143681i
$975$	16.0203	+	9.24933i	0.513061	+	0.296216i
$976$	18.2159	−	16.7508i	0.583078	−	0.536181i
$977$	−6.04122	−	10.4637i	−0.193276	−	0.334763i	0.753058	−	0.657954i	$-0.228578\pi$
$977$	−6.04122	−	10.4637i	−0.193276	−	0.334763i	−0.946334	+	0.323191i	$0.895245\pi$
$978$	4.44214	−	8.77496i	0.142044	−	0.280592i
$979$	−22.0457			−0.704584
$980$		0			0
$981$	−6.80731			−0.217341
$982$	14.4637	−	28.5715i	0.461556	−	0.911755i
$983$	8.67473	+	15.0251i	0.276681	+	0.479225i	0.970558	−	0.240868i	$-0.0774322\pi$
$983$	8.67473	+	15.0251i	0.276681	+	0.479225i	−0.693877	+	0.720094i	$0.744099\pi$
$984$	12.2537	+	14.8910i	0.390632	+	0.474709i
$985$	7.32000	+	4.22620i	0.233235	+	0.134658i
$986$	56.0131	−	3.08276i	1.78382	−	0.0981752i
$987$		0			0
$988$	−2.51330	−	22.7639i	−0.0799588	−	0.724216i
$989$	−10.4625	+	18.1216i	−0.332689	+	0.576235i
$990$	−1.09977	+	0.718306i	−0.0349530	+	0.0228293i
$991$	42.5136	−	24.5452i	1.35049	−	0.779705i	0.362171	−	0.932112i	$-0.382036\pi$
$991$	42.5136	−	24.5452i	1.35049	−	0.779705i	0.988318	+	0.152407i	$0.0487025\pi$
$992$	40.7115	+	10.3387i	1.29259	+	0.328255i
$993$			21.4868i			0.681864i
$994$		0			0
$995$			3.78461i			0.119980i
$996$	−4.41851	+	10.0658i	−0.140006	+	0.318948i
$997$	−7.88043	+	4.54977i	−0.249576	+	0.144093i	−0.619570	−	0.784941i	$-0.712693\pi$
$997$	−7.88043	+	4.54977i	−0.249576	+	0.144093i	0.369994	+	0.929034i	$0.379360\pi$
$998$	−15.0362	−	23.0214i	−0.475963	−	0.728730i
$999$	−2.64335	+	4.57842i	−0.0836320	+	0.144855i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.o.d.19.4		8
4.3	odd	2		588.2.o.b.19.1		8
7.2	even	3		588.2.b.a.391.5		8
7.3	odd	6		588.2.o.b.31.1		8
7.4	even	3		84.2.o.b.31.1	yes	8
7.5	odd	6		588.2.b.b.391.5		8
7.6	odd	2		84.2.o.a.19.4	✓	8
21.2	odd	6		1764.2.b.j.1567.4		8
21.5	even	6		1764.2.b.i.1567.4		8
21.11	odd	6		252.2.bf.f.199.4		8
21.20	even	2		252.2.bf.g.19.1		8
28.3	even	6	inner	588.2.o.d.31.4		8
28.11	odd	6		84.2.o.a.31.4	yes	8
28.19	even	6		588.2.b.a.391.6		8
28.23	odd	6		588.2.b.b.391.6		8
28.27	even	2		84.2.o.b.19.1	yes	8
56.11	odd	6		1344.2.bl.j.703.3		8
56.13	odd	2		1344.2.bl.j.1279.3		8
56.27	even	2		1344.2.bl.i.1279.3		8
56.53	even	6		1344.2.bl.i.703.3		8
84.11	even	6		252.2.bf.g.199.1		8
84.23	even	6		1764.2.b.i.1567.3		8
84.47	odd	6		1764.2.b.j.1567.3		8
84.83	odd	2		252.2.bf.f.19.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.o.a.19.4	✓	8	7.6	odd	2
84.2.o.a.31.4	yes	8	28.11	odd	6
84.2.o.b.19.1	yes	8	28.27	even	2
84.2.o.b.31.1	yes	8	7.4	even	3
252.2.bf.f.19.4		8	84.83	odd	2
252.2.bf.f.199.4		8	21.11	odd	6
252.2.bf.g.19.1		8	21.20	even	2
252.2.bf.g.199.1		8	84.11	even	6
588.2.b.a.391.5		8	7.2	even	3
588.2.b.a.391.6		8	28.19	even	6
588.2.b.b.391.5		8	7.5	odd	6
588.2.b.b.391.6		8	28.23	odd	6
588.2.o.b.19.1		8	4.3	odd	2
588.2.o.b.31.1		8	7.3	odd	6
588.2.o.d.19.4		8	1.1	even	1	trivial
588.2.o.d.31.4		8	28.3	even	6	inner
1344.2.bl.i.703.3		8	56.53	even	6
1344.2.bl.i.1279.3		8	56.27	even	2
1344.2.bl.j.703.3		8	56.11	odd	6
1344.2.bl.j.1279.3		8	56.13	odd	2
1764.2.b.i.1567.3		8	84.23	even	6
1764.2.b.i.1567.4		8	21.5	even	6
1764.2.b.j.1567.3		8	84.47	odd	6
1764.2.b.j.1567.4		8	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.26175 + 0.638735i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.18404 + 1.61185i) q^{4} +(-0.380152 - 0.219481i) q^{5} +(0.0777157 + 1.41208i) q^{6} +(0.464416 + 2.79004i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.26175 + 0.638735i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.18404 + 1.61185i) q^{4} +(-0.380152 - 0.219481i) q^{5} +(0.0777157 + 1.41208i) q^{6} +(0.464416 + 2.79004i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.339468 - 0.519747i) q^{10} +(-1.83249 + 1.05799i) q^{11} +(-0.803884 + 1.83133i) q^{12} +3.84803i q^{13} -0.438962i q^{15} +(-1.19612 + 3.81698i) q^{16} +(4.89158 - 2.82415i) q^{17} +(-1.18404 + 0.773342i) q^{18} +(-1.48792 + 2.57715i) q^{19} +(-0.0963438 - 0.872621i) q^{20} +(-2.98792 + 0.164445i) q^{22} +(4.13127 + 2.38519i) q^{23} +(-2.18404 + 1.79722i) q^{24} +(-2.40366 - 4.16325i) q^{25} +(-2.45787 + 4.85526i) q^{26} -1.00000 q^{27} +7.02285 q^{29} +(0.280380 - 0.553861i) q^{30} +(-3.71264 - 6.43048i) q^{31} +(-3.94724 + 4.05208i) q^{32} +(-1.83249 - 1.05799i) q^{33} +(7.97584 - 0.438962i) q^{34} +(-1.98792 + 0.219481i) q^{36} +(2.64335 - 4.57842i) q^{37} +(-3.52350 + 2.30134i) q^{38} +(-3.33249 + 1.92401i) q^{39} +(0.435811 - 1.16257i) q^{40} -6.81813i q^{41} +4.38646i q^{43} +(-3.87505 - 1.70100i) q^{44} +(0.380152 - 0.219481i) q^{45} +(3.68914 + 5.64831i) q^{46} +(-0.844569 + 1.46284i) q^{47} +(-3.90366 + 0.872621i) q^{48} +(-0.373604 - 6.78829i) q^{50} +(4.89158 + 2.82415i) q^{51} +(-6.20244 + 4.55620i) q^{52} +(-5.35599 - 9.27685i) q^{53} +(-1.26175 - 0.638735i) q^{54} +0.928833 q^{55} -2.97584 q^{57} +(8.86109 + 4.48574i) q^{58} +(4.05909 + 7.03055i) q^{59} +(0.707540 - 0.519747i) q^{60} +(-5.35787 - 3.09337i) q^{61} +(-0.577061 - 10.4851i) q^{62} +(-7.56863 + 2.59148i) q^{64} +(0.844569 - 1.46284i) q^{65} +(-1.63637 - 2.50539i) q^{66} +(6.79878 - 3.92528i) q^{67} +(10.3439 + 4.54058i) q^{68} +4.77038i q^{69} -1.16982i q^{71} +(-2.64845 - 0.992823i) q^{72} +(8.69036 - 5.01738i) q^{73} +(6.25965 - 4.08843i) q^{74} +(2.40366 - 4.16325i) q^{75} +(-5.91574 + 0.653140i) q^{76} +(-5.43371 + 0.299052i) q^{78} +(-13.4958 - 7.79180i) q^{79} +(1.29246 - 1.18851i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.35498 - 8.60279i) q^{82} +5.49645 q^{83} -2.47939 q^{85} +(-2.80178 + 5.53462i) q^{86} +(3.51142 + 6.08197i) q^{87} +(-3.80287 - 4.62137i) q^{88} +(9.02285 + 5.20934i) q^{89} +(0.619848 - 0.0341142i) q^{90} +(1.04701 + 9.48314i) q^{92} +(3.71264 - 6.43048i) q^{93} +(-2.00000 + 1.30628i) q^{94} +(1.13127 - 0.653140i) q^{95} +(-5.48282 - 1.39237i) q^{96} -2.22605i q^{97} -2.11598i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 4 q^{3} - q^{4} + 2 q^{6} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + q^2 + 4 * q^3 - q^4 + 2 * q^6 + 4 * q^8 - 4 * q^9	\( 8 q + q^{2} + 4 q^{3} - q^{4} + 2 q^{6} + 4 q^{8} - 4 q^{9} + 5 q^{10} + 6 q^{11} + q^{12} - 17 q^{16} + q^{18} + 6 q^{19} - 22 q^{20} - 6 q^{22} - 7 q^{24} + 2 q^{25} - 18 q^{26} - 8 q^{27} - 16 q^{29} + 13 q^{30} - 6 q^{31} - 9 q^{32} + 6 q^{33} + 28 q^{34} + 2 q^{36} + 6 q^{37} - 10 q^{38} - 6 q^{39} + 17 q^{40} - 23 q^{44} + 24 q^{46} - 4 q^{47} - 10 q^{48} + 2 q^{50} - 16 q^{52} - 4 q^{53} - q^{54} + 8 q^{55} + 12 q^{57} + 37 q^{58} + 14 q^{59} - 23 q^{60} - 12 q^{61} + 48 q^{62} + 2 q^{64} + 4 q^{65} + 15 q^{66} + 42 q^{67} + 26 q^{68} - 11 q^{72} + 18 q^{73} - 10 q^{74} - 2 q^{75} - 44 q^{76} - 6 q^{78} - 6 q^{79} + 39 q^{80} - 4 q^{81} + 10 q^{82} - 4 q^{83} - 32 q^{85} + 36 q^{86} - 8 q^{87} - 37 q^{88} + 8 q^{90} - 28 q^{92} + 6 q^{93} - 16 q^{94} - 24 q^{95} - 21 q^{96}+O(q^{100}) \) 8 * q + q^2 + 4 * q^3 - q^4 + 2 * q^6 + 4 * q^8 - 4 * q^9 + 5 * q^10 + 6 * q^11 + q^12 - 17 * q^16 + q^18 + 6 * q^19 - 22 * q^20 - 6 * q^22 - 7 * q^24 + 2 * q^25 - 18 * q^26 - 8 * q^27 - 16 * q^29 + 13 * q^30 - 6 * q^31 - 9 * q^32 + 6 * q^33 + 28 * q^34 + 2 * q^36 + 6 * q^37 - 10 * q^38 - 6 * q^39 + 17 * q^40 - 23 * q^44 + 24 * q^46 - 4 * q^47 - 10 * q^48 + 2 * q^50 - 16 * q^52 - 4 * q^53 - q^54 + 8 * q^55 + 12 * q^57 + 37 * q^58 + 14 * q^59 - 23 * q^60 - 12 * q^61 + 48 * q^62 + 2 * q^64 + 4 * q^65 + 15 * q^66 + 42 * q^67 + 26 * q^68 - 11 * q^72 + 18 * q^73 - 10 * q^74 - 2 * q^75 - 44 * q^76 - 6 * q^78 - 6 * q^79 + 39 * q^80 - 4 * q^81 + 10 * q^82 - 4 * q^83 - 32 * q^85 + 36 * q^86 - 8 * q^87 - 37 * q^88 + 8 * q^90 - 28 * q^92 + 6 * q^93 - 16 * q^94 - 24 * q^95 - 21 * q^96

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